Wavefront optimization for tuning scanner based on performance matching

ABSTRACT

A method for determining a wavefront parameter of a patterning process. The method includes obtaining a reference performance (e.g., a contour, EPE, CD) of a reference apparatus (e.g., a scanner), a lens model for a patterning apparatus configured to convert a wavefront parameter of a wavefront to actuator movement, and a lens fingerprint of a tuning apparatus (e.g., a to-be-matched scanner). Further, the method involves determining the wavefront parameter (e.g., a wavefront parameter such as tilt, offset, etc.) based on the lens fingerprint of the tuning apparatus, the lens model, and a cost function, wherein the cost function is a difference between the reference performance and a tuning apparatus performance.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the U.S. national phase entry of PCT PatentApplication No. PCT/EP2019/066446, which was filed on Jun. 21, 2019,which claims the benefit of priority of U.S. Patent Application No.62/689,482, which was filed on Jun. 25, 2018, and U.S. PatentApplication No. 62/861,673 which was filed on Jun. 14, 2019, each ofwhich is incorporated herein in its entirety by reference.

TECHNICAL FIELD

The description herein relates generally to apparatus and methods of anoptimization process and determining optimum wavefront for a tuningscanner corresponding to a reference performance.

BACKGROUND

A lithographic projection apparatus can be used, for example, in themanufacture of integrated circuits (ICs). In such a case, a patterningdevice (e.g., a mask) may contain or provide a pattern corresponding toan individual layer of the IC (“design layout”), and this pattern can betransferred onto a target portion (e.g. comprising one or more dies) ona substrate (e.g., silicon wafer) that has been coated with a layer ofradiation-sensitive material (“resist”), by methods such as irradiatingthe target portion through the pattern on the patterning device. Ingeneral, a single substrate contains a plurality of adjacent targetportions to which the pattern is transferred successively by thelithographic projection apparatus, one target portion at a time. In onetype of lithographic projection apparatuses, the pattern on the entirepatterning device is transferred onto one target portion in one go; suchan apparatus is commonly referred to as a stepper. In an alternativeapparatus, commonly referred to as a step-and-scan apparatus, aprojection beam scans over the patterning device in a given referencedirection (the “scanning” direction) while synchronously moving thesubstrate parallel or anti-parallel to this reference direction.Different portions of the pattern on the patterning device aretransferred to one target portion progressively. Since, in general, thelithographic projection apparatus will have a reduction ratio M (e.g.,4), the speed F at which the substrate is moved will be 1/M times thatat which the projection beam scans the patterning device. Moreinformation with regard to lithographic devices as described herein canbe gleaned, for example, from U.S. Pat. No. 6,046,792, incorporatedherein by reference.

Prior to transferring the pattern from the patterning device to thesubstrate, the substrate may undergo various procedures, such aspriming, resist coating and a soft bake. After exposure, the substratemay be subjected to other procedures (“post-exposure procedures”), suchas a post-exposure bake (PEB), development, a hard bake andmeasurement/inspection of the transferred pattern. This array ofprocedures is used as a basis to make an individual layer of a device,e.g., an IC. The substrate may then undergo various processes such asetching, ion-implantation (doping), metallization, oxidation,chemo-mechanical polishing, etc., all intended to finish off theindividual layer of the device. If several layers are required in thedevice, then the whole procedure, or a variant thereof, is repeated foreach layer. Eventually, a device will be present in each target portionon the substrate. These devices are then separated from one another by atechnique such as dicing or sawing, whence the individual devices can bemounted on a carrier, connected to pins, etc.

Thus, manufacturing devices, such as semiconductor devices, typicallyinvolves processing a substrate (e.g., a semiconductor wafer) using anumber of fabrication processes to form various features and multiplelayers of the devices. Such layers and features are typicallymanufactured and processed using, e.g., deposition, lithography, etch,chemical-mechanical polishing, and ion implantation. Multiple devicesmay be fabricated on a plurality of dies on a substrate and thenseparated into individual devices. This device manufacturing process maybe considered a patterning process. A patterning process involves apatterning step, such as optical and/or nanoimprint lithography using apatterning device in a lithographic apparatus, to transfer a pattern onthe patterning device to a substrate and typically, but optionally,involves one or more related pattern processing steps, such as resistdevelopment by a development apparatus, baking of the substrate using abake tool, etching using the pattern using an etch apparatus, etc.

As noted, lithography is a central step in the manufacturing of devicesuch as ICs, where patterns formed on substrates define functionalelements of the devices, such as microprocessors, memory chips, etc.Similar lithographic techniques are also used in the formation of flatpanel displays, micro-electro mechanical systems (MEMS) and otherdevices.

As semiconductor manufacturing processes continue to advance, thedimensions of functional elements have continually been reduced whilethe amount of functional elements, such as transistors, per device hasbeen steadily increasing over decades, following a trend commonlyreferred to as “Moore's law”. At the current state of technology, layersof devices are manufactured using lithographic projection apparatusesthat project a design layout onto a substrate using illumination from adeep-ultraviolet illumination source, creating individual functionalelements having dimensions well below 100 nm, i.e. less than half thewavelength of the radiation from the illumination source (e.g., a 193 nmillumination source).

This process in which features with dimensions smaller than theclassical resolution limit of a lithographic projection apparatus areprinted, is commonly known as low-k₁ lithography, according to theresolution formula CD=k₁×λ/NA, where λ is the wavelength of radiationemployed (currently in most cases 248 nm or 193 nm), NA is the numericalaperture of projection optics in the lithographic projection apparatus,CD is the “critical dimension”—generally the smallest feature sizeprinted—and k₁ is an empirical resolution factor. In general, thesmaller k₁ the more difficult it becomes to reproduce a pattern on thesubstrate that resembles the shape and dimensions planned by a designerin order to achieve particular electrical functionality and performance.To overcome these difficulties, sophisticated fine-tuning steps areapplied to the lithographic projection apparatus, the design layout, orthe patterning device. These include, for example, but not limited to,optimization of NA and optical coherence settings, customizedillumination schemes, use of phase shifting patterning devices, opticalproximity correction (OPC, sometimes also referred to as “optical andprocess correction”) in the design layout, or other methods generallydefined as “resolution enhancement techniques” (RET). The term“projection optics” as used herein should be broadly interpreted asencompassing various types of optical systems, including refractiveoptics, reflective optics, apertures and catadioptric optics, forexample. The term “projection optics” may also include componentsoperating according to any of these design types for directing, shapingor controlling the projection beam of radiation, collectively orsingularly. The term “projection optics” may include any opticalcomponent in the lithographic projection apparatus, no matter where theoptical component is located on an optical path of the lithographicprojection apparatus. Projection optics may include optical componentsfor shaping, adjusting and/or projecting radiation from the sourcebefore the radiation passes the patterning device, and/or opticalcomponents for shaping, adjusting and/or projecting the radiation afterthe radiation passes the patterning device. The projection opticsgenerally exclude the source and the patterning device.

SUMMARY

According to an embodiment, there is provided a method for determining awavefront of a patterning apparatus of a patterning process. The methodincludes obtaining (i) a reference performance of a reference apparatus,(ii) a lens model of a patterning apparatus configured to convert awavefront parameter of a wavefront to actuator movements, and (iii) alens fingerprint of a tuning scanner, and determining, via a processor,the wavefront parameter based on the lens fingerprint of the tuningscanner, the lens model, and a cost function, wherein the cost functionis a difference between the reference performance and a tuning scannerperformance.

In an embodiment, the determining of the wavefront parameter is aniterative process. An iteration includes generating, via simulation ofthe lens model using the lens fingerprint of the tuning scanner, aninitial wavefront, determining a substrate pattern from the initialwavefront, determining the tuning performance from the substratepattern, evaluating the cost function based on the tuning performanceand the reference performance, and adjusting the wavefront parameter ofthe initial wavefront based on a gradient of the cost function, suchthat the cost function is improved.

In an embodiment, the wavefront comprises the lens fingerprint of thetuning scanner and a performance fingerprint of the lens model.

In an embodiment, the adjusting of the wavefront parameter is furtherbased on the performance fingerprint of the lens model.

In an embodiment, determining the substrate pattern comprises simulationof a process model of the patterning process using the initial wavefrontor the adjusted wavefront.

In an embodiment, the process model includes a mask model configured topredict a mask image based from a mask pattern, an optical modelconfigured to predict an aerial image from the mask pattern, and/or aresist model configured to predict a resist image from the aerial image.

In an embodiment, determining the substrate pattern includes receiving,via a metrology tool, substrate measurements of an exposed substrate,wherein the substrate is exposed using the initial wavefront or theadjusted wavefront; and determining the substrate pattern based oncontour extraction from the substrate measurement.

In an embodiment, the cost function is minimized or maximized.

In an embodiment, the cost function is an edge placement error, CDand/or an error within a tolerance band of edge placement.

In an embodiment, the lens model includes constraints related to acorrection limitation of a tuning scanner corresponding to a wavefrontparameter.

In an embodiment, the wavefront parameter comprises an offset, a tiltand/or a curvature of an optical system of the patterning apparatus.

In an embodiment, the wavefront is a through-slit wavefront.

In an embodiment, the slit has a rectangular shape.

In an embodiment, the wavefront is represented by Zernike polynomialacross a slit.

In an embodiment, the wavefront parameter is expressed as a vector ofZernike coefficients.

In an embodiment, the method further includes converting, via the lensmodel, the wavefront parameters to the actuator movements, and actuatingthe optical system of the tuning scanner based on the actuatormovements.

In an embodiment, the reference performance and the tuning scannerperformance are expressed in terms of a contour of a pattern and/or acritical dimension.

According to an embodiment, there is provided a method for determining awavefront of a tuning scanner with respect to a reference apparatus. Themethod includes obtaining (i) a reference performance of the referenceapparatus corresponding to a reference lens fingerprint, and (ii) a lensfingerprint of a tuning scanner; determining, via a processor, awavefront parameter of the tuning scanner based on the lens fingerprintand a cost function, wherein the cost function computes a differencebetween the reference performance and a tuning scanner performance.

In an embodiment, obtaining the reference performance includes measuringthe reference lens fingerprint of the reference apparatus; generating,via simulation of a process model, a reference pattern based on themeasured lens fingerprint of the reference apparatus and a patterningdevice pattern corresponding to a design layout; and determining thereference performance based on a contour of the reference pattern.

In an embodiment, the determining of the wavefront parameter is aniterative process. An iteration includes determining via simulation ofthe process model, a substrate pattern using a patterning device patternand a lens fingerprint of the tuning scanner; determining the tuningscanner performance based on the substrate pattern; evaluating the costfunction based on the tuning scanner performance and the referenceperformance; and adjusting the wavefront parameter based on a gradientof the cost function with respect to the wavefront parameter, such thatthe cost function is improved.

In an embodiment, the patterning device pattern is generated viasimulation of a mask optimization or source mask optimization process,wherein a lens aberration model is included in the process model.

In an embodiment, the reference performance and tuning scannerperformance is expressed in terms of a contour of a pattern, and/or acritical dimension.

In an embodiment, the reference apparatus includes a scanner of a waferfabrication facility, an ideal scanner having no aberrations, and/or anaberration compensated scanner that is compensated for averageaberration of a plurality of scanners within the wafer fabricationfacility.

In an embodiment, the cost function is an edge placement error, CDand/or an error within a tolerance band of edge placement.

In an embodiment, the wavefront parameter comprises an offset, a tilt, acurvature, and/or and up to and including third order parametersassociated with an optical system of the patterning apparatus.

Furthermore, according to an embodiment, there is provided a method ofwavefront matching of a tuning scanner for a patterning process. Themethod includes obtaining (i) a plurality of hot spot patternscorresponding to a layer of a substrate, (ii) a plurality of wavefrontscorresponding to the plurality of hot spot patterns, and (iii) a lensfingerprint of a tuning scanner; determining, via simulation of apatterning process using the lens fingerprint, a tuning scannerperformance; and selecting a wavefront parameter for the tuning scannerfrom the plurality of wavefronts based on comparison between the tuningscanner performance and a reference performance.

In an embodiment, one or more of the plurality of wavefronts includeoptimized wavefront parameters.

In an embodiment, the one or more of the plurality of wavefronts isassociated with a particular reference performance.

Furthermore, according to an embodiment, there is provided a method ofdetermining a lens adjustment parameter value for a patterning apparatusused in a patterning process. The method involves obtaining (i) a pupilweight map associated with an exposure wavefront, where weights of thepupil weight map are associated with a performance metric of thepatterning apparatus, and (ii) a lens model of a patterning apparatus,the lens model configured to convert an aberration wavefront parameterassociated with the exposure wavefront to a lens adjustment parameter;determining, via executing the lens model using the pupil weight map andthe exposure wavefront, a lens adjustment parameter value such that alens model merit function associated with the lens model is improved,where the lens model merit function is a function of the pupil weightmap; and adjusting, via simulating a patterning process using theaberration wavefront associated with the lens adjustment parametervalue, the weights of the pupil weight map such that the performancemetric of the patterning process is improved, the performance metricbeing a function of an edge placement error and a pattern placementerror associated with a pattern to be printed on a substrate.

Furthermore, according to an embodiment, there is provided a method ofdetermining lens actuator setting for a patterning apparatus. The methodincludes obtaining a lens merit function and a reference value (e.g., annon-zero integer) assigned to a residual aberration wavefront associatedwith the patterning apparatus; and determining, via a lens model of thepatterning apparatus using the lens merit function and the referencevalue, the lens actuator setting from the lens actuator space of thepatterning apparatus based on minimizing the lens merit function, thelens merit function comprising a lithographic metric associated with theresidual aberration wavefront.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, withreference to the accompanying drawings in which:

FIG. 1 schematically depicts a lithography apparatus, according to anembodiment;

FIG. 2 schematically depicts an embodiment of a lithographic cell orcluster, according to an embodiment;

FIG. 3 is a flow chart of a method for wavefront optimization based on alens model, according to an embodiment;

FIG. 4 illustrate example wavefronts at different locations across aslit generated during wavefront optimization process of FIG. 2 ,according to an embodiment;

FIG. 5 is an example of an ideal performance corresponding to a scannerwith no aberrations, according to an embodiment;

FIG. 6A illustrates an example of a reference contour as a matchingtarget overlapping with the ideal contour of FIG. 5 , according to anembodiment;

FIG. 6B illustrates an example of evaluation points on the referencecontour of FIG. 6A, according to an embodiment;

FIG. 6C illustrates an example of tuning performance matching with thereference contour as a matching target of FIG. 6B, according to anembodiment;

FIG. 7 illustrates a tolerance band for a contour or edge placementerror (EPE) based matching of tuning scanner, according to anembodiment;

FIG. 8 is a flow chart of another method for wavefront optimizationbased on a reference scanner performance, according to an embodiment;

FIG. 9 is a flow chart of a method for determining wavefront for thetuning scanner based hot spot patterns, according an embodiment;

FIG. 10 is a flow chart of simulation of a patterning process, accordingan embodiment;

FIG. 11 is a flow chart of determining hot spot patterns, according anembodiment;

FIG. 12A is example of a pupil optimization, according an embodiment;

FIG. 12B illustrates example lens fingerprint and optimized wavefrontbased on the lens fingerprint, according an embodiment;

FIG. 13A and FIG. 13B describes a method for determining a lensadjustment parameter value for a patterning apparatus used in apatterning process, according an embodiment;

FIG. 14 is an example of a pupil weight map based on a dipole pupil,according an embodiment;

FIGS. 15A and 15B illustrate another example of generating a pupilweight map based on illumination pattern, according an embodiment;

FIG. 16A illustrate an example illumination pupil, according anembodiment;

FIGS. 16B and 16C illustrate an example wavefronts associated with theillumination pupil of FIG. 16A, according an embodiment;

FIG. 17 illustrates example principal components obtained from aprincipal component analysis, according an embodiment;

FIG. 18 is a flow chart of method for determining lens adjustments for apatterning apparatus, according an embodiment;

FIG. 19 is an example of a wavefront target driving the lithographicmetric of a lens model to determine a lens knob sub-space, according anembodiment;

FIG. 20 is a block diagram of an example computer system, according toan embodiment;

FIG. 21 is a schematic diagram of another lithographic projectionapparatus, according to an embodiment;

FIG. 22 is a view of the apparatus in FIG. 1 for an extreme ultra violetscanner, according to an embodiment;

FIG. 23 is a more detailed view of the source collector module SO of theapparatus of FIG. 21 and FIG. 22 , according to an embodiment.

DETAILED DESCRIPTION

Before describing embodiments in detail, it is instructive to present anexample environment in which embodiments may be implemented.

FIG. 1 schematically depicts an embodiment of a lithographic apparatusLA. The apparatus comprises:

-   -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. UV radiation or DUV radiation);    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask) MA and connected to a        first positioner PM configured to accurately position the        patterning device in accordance with certain parameters;    -   a substrate table (e.g. a wafer table) WT (e.g., WTa, WTb or        both) constructed to hold a substrate (e.g. a resist coated        wafer) W and connected to a second positioner PW configured to        accurately position the substrate in accordance with certain        parameters; and    -   a projection system (e.g. a refractive projection lens system)        PS configured to project a pattern imparted to the radiation        beam B by patterning device MA onto a target portion C (e.g.        comprising one or more dies and often referred to as fields) of        the substrate W, the projection system supported on a reference        frame (RF).

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array of a type asreferred to above, or employing a reflective mask).

The illuminator IL receives a beam of radiation from a radiation sourceSO. The source and the lithographic apparatus may be separate entities,for example when the source is an excimer laser. In such cases, thesource is not considered to form part of the lithographic apparatus andthe radiation beam is passed from the source SO to the illuminator ILwith the aid of a beam delivery system BD comprising for examplesuitable directing mirrors and/or a beam expander. In other cases thesource may be an integral part of the apparatus, for example when thesource is a mercury lamp. The source SO and the illuminator IL, togetherwith the beam delivery system BD if required, may be referred to as aradiation system.

The illuminator IL may alter the intensity distribution of the beam. Theilluminator may be arranged to limit the radial extent of the radiationbeam such that the intensity distribution is non-zero within an annularregion in a pupil plane of the illuminator IL. Additionally oralternatively, the illuminator IL may be operable to limit thedistribution of the beam in the pupil plane such that the intensitydistribution is non-zero in a plurality of equally spaced sectors in thepupil plane. The intensity distribution of the radiation beam in a pupilplane of the illuminator IL may be referred to as an illumination mode.

So, the illuminator IL may comprise adjuster AD configured to adjust the(angular/spatial) intensity distribution of the beam. Generally, atleast the outer and/or inner radial extent (commonly referred to asσ-outer and σ-inner, respectively) of the intensity distribution in apupil plane of the illuminator can be adjusted. The illuminator IL maybe operable to vary the angular distribution of the beam. For example,the illuminator may be operable to alter the number, and angular extent,of sectors in the pupil plane wherein the intensity distribution isnon-zero. By adjusting the intensity distribution of the beam in thepupil plane of the illuminator, different illumination modes may beachieved. For example, by limiting the radial and angular extent of theintensity distribution in the pupil plane of the illuminator IL, theintensity distribution may have a multi-pole distribution such as, forexample, a dipole, quadrupole or hexapole distribution. A desiredillumination mode may be obtained, e.g., by inserting an optic whichprovides that illumination mode into the illuminator IL or using aspatial light modulator.

The illuminator IL may be operable alter the polarization of the beamand may be operable to adjust the polarization using adjuster AM. Thepolarization state of the radiation beam across a pupil plane of theilluminator IL may be referred to as a polarization mode. The use ofdifferent polarization modes may allow greater contrast to be achievedin the image formed on the substrate W. The radiation beam may beunpolarized. Alternatively, the illuminator may be arranged to linearlypolarize the radiation beam. The polarization direction of the radiationbeam may vary across a pupil plane of the illuminator IL. Thepolarization direction of radiation may be different in differentregions in the pupil plane of the illuminator IL. The polarization stateof the radiation may be chosen in dependence on the illumination mode.For multi-pole illumination modes, the polarization of each pole of theradiation beam may be generally perpendicular to the position vector ofthat pole in the pupil plane of the illuminator IL. For example, for adipole illumination mode, the radiation may be linearly polarized in adirection that is substantially perpendicular to a line that bisects thetwo opposing sectors of the dipole. The radiation beam may be polarizedin one of two different orthogonal directions, which may be referred toas X-polarized and Y-polarized states. For a quadrupole illuminationmode the radiation in the sector of each pole may be linearly polarizedin a direction that is substantially perpendicular to a line thatbisects that sector. This polarization mode may be referred to as XYpolarization. Similarly, for a hexapole illumination mode the radiationin the sector of each pole may be linearly polarized in a direction thatis substantially perpendicular to a line that bisects that sector. Thispolarization mode may be referred to as TE polarization.

In addition, the illuminator IL generally comprises various othercomponents, such as an integrator IN and a condenser CO. Theillumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

Thus, the illuminator provides a conditioned beam of radiation B, havinga desired uniformity and intensity distribution in its cross section.

The support structure MT supports the patterning device in a manner thatdepends on the orientation of the patterning device, the design of thelithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The support structure can use mechanical, vacuum, electrostatic or otherclamping techniques to hold the patterning device. The support structuremay be a frame or a table, for example, which may be fixed or movable asrequired. The support structure may ensure that the patterning device isat a desired position, for example with respect to the projectionsystem. Any use of the terms “reticle” or “mask” herein may beconsidered synonymous with the more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a pattern in atarget portion of the substrate. In an embodiment, a patterning deviceis any device that can be used to impart a radiation beam with a patternin its cross-section so as to create a pattern in a target portion ofthe substrate. It should be noted that the pattern imparted to theradiation beam may not exactly correspond to the desired pattern in thetarget portion of the substrate, for example if the pattern includesphase-shifting features or so called assist features. Generally, thepattern imparted to the radiation beam will correspond to a particularfunctional layer in a device being created in the target portion, suchas an integrated circuit.

A patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam, which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

The projection system PS has an optical transfer function which may benon-uniform, which can affect the pattern imaged on the substrate W. Forunpolarized radiation such effects can be fairly well described by twoscalar maps, which describe the transmission (apodization) and relativephase (aberration) of radiation exiting the projection system PS as afunction of position in a pupil plane thereof. These scalar maps, whichmay be referred to as the transmission map and the relative phase map,may be expressed as a linear combination of a complete set of basisfunctions. A particularly convenient set is the Zernike polynomials,which form a set of orthogonal polynomials defined on a unit circle. Adetermination of each scalar map may involve determining thecoefficients in such an expansion. Since the Zernike polynomials areorthogonal on the unit circle, the Zernike coefficients may bedetermined by calculating the inner product of a measured scalar mapwith each Zernike polynomial in turn and dividing this by the square ofthe norm of that Zernike polynomial.

The transmission map and the relative phase map are field and systemdependent. That is, in general, each projection system PS will have adifferent Zernike expansion for each field point (i.e. for each spatiallocation in its image plane). The relative phase of the projectionsystem PS in its pupil plane may be determined by projecting radiation,for example from a point-like source in an object plane of theprojection system PS (i.e. the plane of the patterning device MA),through the projection system PS and using a shearing interferometer tomeasure a wavefront (i.e. a locus of points with the same phase). Ashearing interferometer is a common path interferometer and therefore,advantageously, no secondary reference beam is required to measure thewavefront. The shearing interferometer may comprise a diffractiongrating, for example a two dimensional grid, in an image plane of theprojection system (i.e. the substrate table WT) and a detector arrangedto detect an interference pattern in a plane that is conjugate to apupil plane of the projection system PS. The interference pattern isrelated to the derivative of the phase of the radiation with respect toa coordinate in the pupil plane in the shearing direction. The detectormay comprise an array of sensing elements such as, for example, chargecoupled devices (CCDs).

The projection system PS of a lithography apparatus may not producevisible fringes and therefore the accuracy of the determination of thewavefront can be enhanced using phase stepping techniques such as, forexample, moving the diffraction grating. Stepping may be performed inthe plane of the diffraction grating and in a direction perpendicular tothe scanning direction of the measurement. The stepping range may be onegrating period, and at least three (uniformly distributed) phase stepsmay be used. Thus, for example, three scanning measurements may beperformed in the y-direction, each scanning measurement being performedfor a different position in the x-direction. This stepping of thediffraction grating effectively transforms phase variations intointensity variations, allowing phase information to be determined. Thegrating may be stepped in a direction perpendicular to the diffractiongrating (z direction) to calibrate the detector.

The diffraction grating may be sequentially scanned in two perpendiculardirections, which may coincide with axes of a co-ordinate system of theprojection system PS (x and y) or may be at an angle such as 45 degreesto these axes. Scanning may be performed over an integer number ofgrating periods, for example one grating period. The scanning averagesout phase variation in one direction, allowing phase variation in theother direction to be reconstructed. This allows the wavefront to bedetermined as a function of both directions.

The transmission (apodization) of the projection system PS in its pupilplane may be determined by projecting radiation, for example from apoint-like source in an object plane of the projection system PS (i.e.the plane of the patterning device MA), through the projection system PSand measuring the intensity of radiation in a plane that is conjugate toa pupil plane of the projection system PS, using a detector. The samedetector as is used to measure the wavefront to determine aberrationsmay be used.

The projection system PS may comprise a plurality of optical (e.g.,lens) elements and may further comprise an adjustment mechanism AMconfigured to adjust one or more of the optical elements so as tocorrect for aberrations (phase variations across the pupil planethroughout the field). To achieve this, the adjustment mechanism may beoperable to manipulate one or more optical (e.g., lens) elements withinthe projection system PS in one or more different ways. The projectionsystem may have a co-ordinate system wherein its optical axis extends inthe z direction. The adjustment mechanism may be operable to do anycombination of the following: displace one or more optical elements;tilt one or more optical elements; and/or deform one or more opticalelements. Displacement of an optical element may be in any direction (x,y, z or a combination thereof). Tilting of an optical element istypically out of a plane perpendicular to the optical axis, by rotatingabout an axis in the x and/or y directions although a rotation about thez axis may be used for a non-rotationally symmetric aspherical opticalelement. Deformation of an optical element may include a low frequencyshape (e.g. astigmatic) and/or a high frequency shape (e.g. free formaspheres). Deformation of an optical element may be performed forexample by using one or more actuators to exert force on one or moresides of the optical element and/or by using one or more heatingelements to heat one or more selected regions of the optical element. Ingeneral, it may not be possible to adjust the projection system PS tocorrect for apodization (transmission variation across the pupil plane).The transmission map of a projection system PS may be used whendesigning a patterning device (e.g., mask) MA for the lithographyapparatus LA. Using a computational lithography technique, thepatterning device MA may be designed to at least partially correct forapodization.

The lithographic apparatus may be of a type having two (dual stage) ormore tables (e.g., two or more substrate tables WTa, WTb, two or morepatterning device tables, a substrate table WTa and a table WTb belowthe projection system without a substrate that is dedicated to, forexample, facilitating measurement, and/or cleaning, etc.). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure. For example, alignmentmeasurements using an alignment sensor AS and/or level (height, tilt,etc.) measurements using a level sensor LS may be made.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g. water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the patterning device and the projection system. Immersiontechniques are well known in the art for increasing the numericalaperture of projection systems. The term “immersion” as used herein doesnot mean that a structure, such as a substrate, must be submerged inliquid, but rather only means that liquid is located between theprojection system and the substrate during exposure.

So, in operation of the lithographic apparatus, a radiation beam isconditioned and provided by the illumination system IL. The radiationbeam B is incident on the patterning device (e.g., mask) MA, which isheld on the support structure (e.g., mask table) MT, and is patterned bythe patterning device. Having traversed the patterning device MA, theradiation beam B passes through the projection system PS, which focusesthe beam onto a target portion C of the substrate W. With the aid of thesecond positioner PW and position sensor IF (e.g. an interferometricdevice, linear encoder, 2-D encoder or capacitive sensor), the substratetable WT can be moved accurately, e.g. so as to position differenttarget portions C in the path of the radiation beam B. Similarly, thefirst positioner PM and another position sensor (which is not explicitlydepicted in FIG. 1 ) can be used to accurately position the patterningdevice MA with respect to the path of the radiation beam B, e.g. aftermechanical retrieval from a mask library, or during a scan. In general,movement of the support structure MT may be realized with the aid of along-stroke module (coarse positioning) and a short-stroke module (finepositioning), which form part of the first positioner PM. Similarly,movement of the substrate table WT may be realized using a long-strokemodule and a short-stroke module, which form part of the secondpositioner PW. In the case of a stepper (as opposed to a scanner) thesupport structure MT may be connected to a short-stroke actuator only,or may be fixed. Patterning device MA and substrate W may be alignedusing patterning device alignment marks M1, M2 and substrate alignmentmarks P1, P2. Although the substrate alignment marks as illustratedoccupy dedicated target portions, they may be located in spaces betweentarget portions (these are known as scribe-lane alignment marks).Similarly, in situations in which more than one die is provided on thepatterning device MA, the patterning device alignment marks may belocated between the dies.

The depicted apparatus could be used in at least one of the followingmodes:

-   -   1. In step mode, the support structure MT and the substrate        table WT are kept essentially stationary, while an entire        pattern imparted to the radiation beam is projected onto a        target portion C at one time (i.e. a single static exposure).        The substrate table WT is then shifted in the X and/or Y        direction so that a different target portion C can be exposed.        In step mode, the maximum size of the exposure field limits the        size of the target portion C imaged in a single static exposure.    -   2. In scan mode, the support structure MT and the substrate        table WT are scanned synchronously while a pattern imparted to        the radiation beam is projected onto a target portion C (i.e. a        single dynamic exposure). The velocity and direction of the        substrate table WT relative to the support structure MT may be        determined by the (de-)magnification and image reversal        characteristics of the projection system PS. In scan mode, the        maximum size of the exposure field limits the width (in the        non-scanning direction) of the target portion in a single        dynamic exposure, whereas the length of the scanning motion        determines the height (in the scanning direction) of the target        portion.    -   3. In another mode, the support structure MT is kept essentially        stationary holding a programmable patterning device, and the        substrate table WT is moved or scanned while a pattern imparted        to the radiation beam is projected onto a target portion C. In        this mode, generally a pulsed radiation source is employed and        the programmable patterning device is updated as required after        each movement of the substrate table WT or in between successive        radiation pulses during a scan. This mode of operation can be        readily applied to maskless lithography that utilizes        programmable patterning device, such as a programmable mirror        array of a type as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

Although specific reference may be made in this text to the use oflithography apparatus in the manufacture of ICs, it should be understoodthat the lithography apparatus described herein may have otherapplications, such as the manufacture of integrated optical systems,guidance and detection patterns for magnetic domain memories,liquid-crystal displays (LCDs), thin film magnetic heads, etc. Theskilled artisan will appreciate that, in the context of such alternativeapplications, any use of the terms “wafer” or “die” herein may beconsidered as synonymous with the more general terms “substrate” or“target portion”, respectively. The substrate referred to herein may beprocessed, before or after exposure, in for example a track (a tool thattypically applies a layer of resist to a substrate and develops theexposed resist) or a metrology or inspection tool. Where applicable, thedisclosure herein may be applied to such and other substrate processingtools. Further, the substrate may be processed more than once, forexample in order to create a multi-layer IC, so that the term substrateused herein may also refer to a substrate that already contains multipleprocessed layers.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of 365, 248, 193, 157 or 126 nm) and extremeultra-violet (EUV) radiation (e.g. having a wavelength in the range of5-20 nm), as well as particle beams, such as ion beams or electronbeams.

Various patterns on or provided by a patterning device may havedifferent process windows. i.e., a space of processing variables underwhich a pattern will be produced within specification. Examples ofpattern specifications that relate to potential systematic defectsinclude checks for necking, line pull back, line thinning, CD, edgeplacement, overlapping, resist top loss, resist undercut and/orbridging. The process window of all the patterns on a patterning deviceor an area thereof may be obtained by merging (e.g., overlapping)process windows of each individual pattern. The boundary of the processwindow of all the patterns contains boundaries of process windows ofsome of the individual patterns. In other words, these individualpatterns limit the process window of all the patterns. These patternscan be referred to as “hot spots” or “process window limiting patterns(PWLPs),” which are used interchangeably herein. When controlling a partof a patterning process, it is possible and economical to focus on thehot spots. When the hot spots are not defective, it is most likely thatall the patterns are not defective.

As shown in FIG. 2 , the lithographic apparatus LA may form part of alithographic cell LC, also sometimes referred to a lithocell or cluster,which also includes apparatuses to perform pre- and post-exposureprocesses on a substrate. Conventionally these include one or more spincoaters SC to deposit one or more resist layers, one or more developersDE to develop exposed resist, one or more chill plates CH and/or one ormore bake plates BK. A substrate handler, or robot, RO picks up one ormore substrates from input/output port I/O1, I/O2, moves them betweenthe different process apparatuses and delivers them to the loading bayLB of the lithographic apparatus. These apparatuses, which are oftencollectively referred to as the track, are under the control of a trackcontrol unit TCU which is itself controlled by the supervisory controlsystem SCS, which also controls the lithographic apparatus vialithography control unit LACU. Thus, the different apparatuses can beoperated to maximize throughput and processing efficiency.

In order that a substrate that is exposed by the lithographic apparatusis exposed correctly and consistently and/or in order to monitor a partof the patterning process (e.g., a device manufacturing process) thatincludes at least one pattern transfer step (e.g., an opticallithography step), it is desirable to inspect a substrate or otherobject to measure or determine one or more properties such as alignment,overlay (which can be, for example, between structures in overlyinglayers or between structures in a same layer that have been providedseparately to the layer by, for example, a double patterning process),line thickness, critical dimension (CD), focus offset, a materialproperty, etc. Accordingly a manufacturing facility in which lithocellLC is located also typically includes a metrology system MET whichmeasures some or all of the substrates W that have been processed in thelithocell or other objects in the lithocell. The metrology system METmay be part of the lithocell LC, for example it may be part of thelithographic apparatus LA (such as alignment sensor AS).

The one or more measured parameters may include, for example, overlaybetween successive layers formed in or on the patterned substrate,critical dimension (CD) (e.g., critical linewidth) of, for example,features formed in or on the patterned substrate, focus or focus errorof an optical lithography step, dose or dose error of an opticallithography step, optical aberrations of an optical lithography step,etc. This measurement may be performed on a target of the productsubstrate itself and/or on a dedicated metrology target provided on thesubstrate. The measurement can be performed after-development of aresist but before etching or can be performed after-etch.

There are various techniques for making measurements of the structuresformed in the patterning process, including the use of a scanningelectron microscope, an image-based measurement tool and/or variousspecialized tools. As discussed above, a fast and non-invasive form ofspecialized metrology tool is one in which a beam of radiation isdirected onto a target on the surface of the substrate and properties ofthe scattered (diffracted/reflected) beam are measured. By evaluatingone or more properties of the radiation scattered by the substrate, oneor more properties of the substrate can be determined. This may betermed diffraction-based metrology. One such application of thisdiffraction-based metrology is in the measurement of feature asymmetrywithin a target. This can be used as a measure of overlay, for example,but other applications are also known. For example, asymmetry can bemeasured by comparing opposite parts of the diffraction spectrum (forexample, comparing the −1st and +1st orders in the diffraction spectrumof a periodic grating). This can be done as described above and asdescribed, for example, in U.S. patent application publication US2006-066855, which is incorporated herein in its entirety by reference.Another application of diffraction-based metrology is in the measurementof feature width (CD) within a target. Such techniques can use theapparatus and methods described hereafter.

Thus, in a device fabrication process (e.g., a patterning process or alithography process), a substrate or other objects may be subjected tovarious types of measurement during or after the process. Themeasurement may determine whether a particular substrate is defective,may establish adjustments to the process and apparatuses used in theprocess (e.g., aligning two layers on the substrate or aligning thepatterning device to the substrate), may measure the performance of theprocess and the apparatuses, or may be for other purposes. Examples ofmeasurement include optical imaging (e.g., optical microscope),non-imaging optical measurement (e.g., measurement based on diffractionsuch as ASML YieldStar metrology tool, ASML SMASH metrology system),mechanical measurement (e.g., profiling using a stylus, atomic forcemicroscopy (AFM)), and/or non-optical imaging (e.g., scanning electronmicroscopy (SEM)). The SMASH (SMart Alignment Sensor Hybrid) system, asdescribed in U.S. Pat. No. 6,961,116, which is incorporated by referenceherein in its entirety, employs a self-referencing interferometer thatproduces two overlapping and relatively rotated images of an alignmentmarker, detects intensities in a pupil plane where Fourier transforms ofthe images are caused to interfere, and extracts the positionalinformation from the phase difference between diffraction orders of thetwo images which manifests as intensity variations in the interferedorders.

Metrology results may be provided directly or indirectly to thesupervisory control system SCS. If an error is detected, an adjustmentmay be made to exposure of a subsequent substrate (especially if theinspection can be done soon and fast enough that one or more othersubstrates of the batch are still to be exposed) and/or to subsequentexposure of the exposed substrate. Also, an already exposed substratemay be stripped and reworked to improve yield, or discarded, therebyavoiding performing further processing on a substrate known to befaulty. In a case where only some target portions of a substrate arefaulty, further exposures may be performed only on those target portionswhich are good.

Within a metrology system MET, a metrology apparatus is used todetermine one or more properties of the substrate, and in particular,how one or more properties of different substrates vary or differentlayers of the same substrate vary from layer to layer. As noted above,the metrology apparatus may be integrated into the lithographicapparatus LA or the lithocell LC or may be a stand-alone device.

To enable the metrology, one or more targets can be provided on thesubstrate. In an embodiment, the target is specially designed and maycomprise a periodic structure. In an embodiment, the target is a part ofa device pattern, e.g., a periodic structure of the device pattern. Inan embodiment, the device pattern is a periodic structure of a memorydevice (e.g., a Bipolar Transistor (BPT), a Bit Line Contact (BLC), etc.structure).

In an embodiment, the target on a substrate may comprise one or more 1-Dperiodic structures (e.g., gratings), which are printed such that afterdevelopment, the periodic structural features are formed of solid resistlines. In an embodiment, the target may comprise one or more 2-Dperiodic structures (e.g., gratings), which are printed such that afterdevelopment, the one or more periodic structures are formed of solidresist pillars or vias in the resist. The bars, pillars or vias mayalternatively be etched into the substrate (e.g., into one or morelayers on the substrate).

The fabrication process (e.g., FIG. 2 ) includes more than one scanner(i.e., a lithographic apparatus) exhibiting different performances(e.g., in terms of patterns printed on a substrate). To provideconsistent performance (e.g., consistent contour or CD) betweendifferent scanners or with respect to a reference performance, awavefront optimization may be performed according to methods of thepresent disclosure.

In an embodiment, an optimization can be performed using, for example,an objective function, such as

$\begin{matrix}{{C{F\left( {z_{1},z_{2},\ldots,z_{N}} \right)}} = {\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}\left( {z_{1},z_{2},\ldots,z_{N}} \right)}}}} & (1)\end{matrix}$

wherein (z₁, z₂, . . . , z_(N)) are N design variables or valuesthereof; f_(p)(z₁, z₂, . . . , z_(N)) may be a function of a differencebetween an actual value and an intended value of a characteristic at thep-th evaluation point for a set of values of the design variables of(z₁, z₂, . . . , z_(N)). w_(p) is a weight constant assigned to the p-thevaluation point. An evaluation point or pattern more critical thanothers can be assigned a higher w_(p) value. Patterns and/or evaluationpoints with larger number of occurrences may be assigned a higher w_(p)value, too. Examples of the evaluation points can be any physical pointor pattern on the substrate, or any point on a patterning devicepattern, or resist image, or aerial image.

The objective function may represent any suitable characteristics of thepatterning process, such as of the lithographic projection apparatus orthe substrate, for instance, focus, CD, image shift, image distortion,image rotation, etc. For example, the objective function may be afunction of one or more of the following lithographic metrics: edgeplacement error, critical dimension, resist contour distance, worstdefect size, pattern shift, stochastic effect, three-dimensional effectof the patterning device, three-dimensional effect of the resist, bestfocus shift, pupil fill factor, exposure time, and/or throughput. Sinceit is the resist image that often dictates the pattern on a substrate,the objective function often includes functions that represent somecharacteristics of the resist image. For example, f_(p) (z₁, z₂, . . . ,z_(N)) of such an evaluation point can be simply a distance between apoint in the resist image to an intended position of that point (i.e.,edge placement error EPE_(p)(z₁, z₂, . . . , z_(N))). The designvariables can be any adjustable parameters such as adjustable parametersof the wavefront.

The lithographic apparatus may include one or more componentscollectively called a “wavefront manipulator” that can be used to adjustshapes of a wavefront, intensity distribution, and/or phase shift of theradiation beam. The wavefront can be adjusted at any location along anoptical path of the lithographic projection apparatus, such as beforethe patterning device, near a pupil plane, near an image plane, or neara focal plane. The projection optics can be used to correct orcompensate for certain distortions of the wavefront caused by, forexample, the illumination, the patterning device, temperature variationin the lithographic projection apparatus, and/or thermal expansion ofcomponents of the lithographic projection apparatus. Adjusting thewavefront can change values of the evaluation points and the objectivefunction. Such changes can be simulated from a model or actuallymeasured.

It should be noted that the normal weighted root mean square (RMS) off_(p)(z₁, z₂, . . . , z_(N)) is defined as

$\sqrt{\frac{1}{P}{\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}\left( {z_{1},z_{2},\ldots,z_{N}} \right)}}}},$therefore, for example, minimizing the weighted RMS of f_(p) (z₁, z₂, .. . , z_(N)) is equivalent to minimizing the objective function

${{C{F\left( {z_{1},z_{2},\ldots,z_{N}} \right)}} = {\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}\left( {z_{1},z_{2},\ldots,z_{N}} \right)}}}},$defined in Eq. 1. Thus the weighted RMS of f_(p)(z₁, z₂, . . . , z_(N))and Eq. 1 may be utilized interchangeably for notational simplicityherein.

The optimization process is to find a set of values of the designvariables, under the constraints (z₁, z₂, . . . , z_(N))∈Z, that, e.g.,minimize the objective function, i.e., to find

$\begin{matrix}{\left( {{\overset{˜}{z}}_{1},{\overset{˜}{z}}_{2},\ldots,{\overset{˜}{z}}_{N}} \right) = {{\arg\min\limits_{{({z_{1},z_{2},\ldots,z_{N}})} \in Z}{{CF}\left( {z_{1},z_{2},\ldots,z_{N}} \right)}} = {\arg\min\limits_{{({z_{1},z_{2},\ldots,z_{N}})} \in Z}{\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}\left( {z_{1},z_{2},\ldots,z_{N}} \right)}}}}}} & (2)\end{matrix}$

The optimization does not necessarily lead to a single set of values forthe design variables (e.g., wavefront parameters). In addition, theremay be physical restraints caused by factors such as the pupil fillfactor, the resist chemistry, the throughput, etc. The optimization mayprovide multiple sets of values for the design variables and associatedperformance characteristics (e.g., the throughput) and allows a user ofthe lithographic apparatus to pick one or more sets.

In an embodiment, an algorithm, such as the Gauss-Newton algorithm, theLevenberg-Marquardt algorithm, the gradient descent algorithm, simulatedannealing, the genetic algorithm, etc. can be applied to evaluate andsolve the objective function.

According to present disclosure, FIGS. 3, 8 and 9 illustrate flow chartsof methods for wavefront determination of a tuning scanner. A tuningscanner or a tuning apparatus refers to any apparatus of a patterningprocess whose wavefront is adjusted such that a performance of thetuning apparatus closely matches a reference performance (e.g., morethan 90% contour-to-contour matching). In an embodiment, the tuningscanner may be referred as a to-be-matched scanner. In an embodiment,the wavefront determination is an iterative process (also referred aswavefront optimization process), where the wavefront of the tuningscanner is progressively modified until a tuning performance (i.e., theperformance of the tuning scanner) closely matches the referenceperformance. In an embodiment, the wavefront is a through-slit wavefront(e.g., a wavefront generated when light is projected across arectangular slit).

In the present disclosure, a wavefront may be interchangeably referredas wavefront parameters, which define the wavefront. For example, thewavefront parameters may be Zernike coefficients, when the wavefront isrepresented by Zernike polynomial. Although Zernike polynomials are usedby way of example to represent a wavefront, it does not limit the scopeof the invention and any other model or representation may be used torepresent a wavefront.

FIG. 3 is a flow chart of a method 3000 for determining a wavefront at alocation across a slit of a tuning apparatus based on a lens model. Inan embodiment, a lens model can be any model that characterizes abehavior of a lens. In an embodiment, the lens model may be a physicsbased mathematical model, an empirical model, a machine learning model,or a combination thereof. The present disclosure is not limited to thetype of lens model. In an embodiment, the lens model may represent anoptical system/projection system of a lithographic apparatus. In anembodiment, the lens model generates wavefronts corresponding to thetuning scanner. In the method 3000, the generated wavefronts are furtherused to determine the tuning performance, match the tuning performancewith the reference performance and iteratively determine wavefrontparameters so that the tuning performance closely matches the referenceperformance. In an embodiment, the reference performance and the tuningscanner performance are expressed in terms of a contour of a patternand/or a critical dimension. The different process involved in themethod 3000 are further discussed in detail below.

Process P301 involves obtaining a lens model 3001 of a patterningapparatus configured to convert a wavefront parameter of a wavefront toactuator movements, a lens fingerprint 3002 (e.g., using a shearinginterferometer) of a tuning scanner, and a reference performance 3007 ofa reference apparatus.

The lens model 3001 may be any model configured to convert a wavefrontparameter of a wavefront to actuator movements of optical elements ofthe tuning scanner. The lens model includes constraints related to acorrection limitation of the tuning scanner corresponding to a wavefrontparameter. In an embodiment, the wavefront parameter may be related to atilt, offset, curvature of the wavefront, or a combination thereof. Thelens 3001 converts the wavefront to the corresponding actuator movementsrelated to change in tilt, offset and/or curvature of the opticalelements. Thus, the lens model 3001 accounts for an optical set-up andadjustment mechanisms (and its limitations/constraints) corresponding tothe tuning scanner. Accordingly, the lens model 3001 may generatedifferent wavefronts for different scanners, thus enabling a customizedwavefront solution corresponding to the tuning scanner.

The lens fingerprint 3002 of a tuning scanner refers to aberrations ofthe tuning scanner. The lens fingerprint 3002 is typically acharacteristic of the projection system (or optical system) of thetuning scanner. Based on the lens fingerprint 3002, a first wavefront(or a first set of wavefronts) may be produced at a first tuning scannerthat further determines a first performance of the first tuning scanner.Similarly, a second wavefront may be produced at a second scanner thatfurther determines a second performance, which may be different from thefirst performance. Such a difference in performance may be undesirable,as it leads to inconsistency in patterns produced within a wafer.

In an embodiment, the lens fingerprint 3002 may be included in a processmodel to generate simulated wafer patterns. Based on such simulatedwafer patterns, a performance of the tuning scanner may be determined.In an embodiment, the lens fingerprint 3002 may be measured via ametrology tool, as mentioned earlier. In another embodiment, the tuningperformance (e.g., a contour) may be determined from a printed waferthat is exposed at the tuning scanner.

The reference performance 3007 may be an ideal performance (e.g.,discussed with FIG. 5 ), or a reference performance (e.g., discussedwith FIGS. 6A-6C) corresponding to a reference apparatus, or aperformance corresponding to another tuning scanner. The referenceperformance 3007 is used in process P307 to compare with the tuningperformance and further determine the wavefront parameters for thetuning scanner. The reference performance 3007 may be expressed in termsof contours, CD, or other parameters of the patterning process that maybe affected by or related to a wavefront.

Process P303 involves determining, via a processor (e.g., a processor104 of FIG. 20 ) a wavefront 3003 (interchangeably referred as wavefrontparameters 3003). In an embodiment, the determining of the wavefrontparameter is based on the lens fingerprint 3002 of the tuning scanner,the lens model 3001, and a cost function. The cost function is adifference between a reference performance (e.g., 3007) and a tuningscanner performance. In an embodiment, a tuning scanner performance 3005may be obtained from simulation of a patterning process, as discussed inprocesses P305. The simulated performance is further used to evaluatethe cost function, as discussed in process P307. In an embodiment, thewavefront 3003 may be an initial wavefront 3003 or an adjusted wavefront3003 generated during an iteration of wavefront optimization so that thetuning performance 3005 closely matches the reference performance 3007(e.g., more than 90% contour-to-contour matching).

In an embodiment, the wavefront 3003 at a particular location along aslit may be defined using Zernike polynomial as follow:W(ρ,θ)=Z _(j) R _(j)(ρ,θ)

Where, W(ρ,θ) is a wavefront at a specific location across the slit, jis an index for the j-th Zernike polynomial (e.g., a Noll index), Z_(j)is a Zernike coefficient (i.e., a wavefront parameter) representative ofthe contribution of the j-th Zernike polynomial to the wavefront, andR_(j)(ρ, θ) is a polynomial expression characterizing j-th Zernike. Inan embodiment, the wavefront parameter is expressed as a vector of suchZernike coefficients.

According to an embodiment, determining the wavefront parameter is aniterative process (e.g., involving processes P305, P307, P309, andP311). An iteration includes generating, via simulation of the lensmodel 3001 using the lens fingerprint 3002 of the tuning scanner, aninitial wavefront 3003 or a set of initial wavefronts (e.g., 4003 ofFIG. 4 ) across different location of a slit, determining a substratepattern (e.g., 6016 of FIG. 6C) or a set of substrate patterns resultingfrom the initial wavefront 3003 (e.g., as discussed in process P307),determining the tuning performance (e.g., 6016 of FIG. 6 ) from thesubstrate pattern, evaluating the cost function based on the tuningperformance and the reference performance 3007 (e.g., as discussed inprocess P307), and adjusting the wavefront parameter of the initialwavefront 3003 based on a gradient of the cost function, such that thecost function is improved (e.g., as discussed in process P311).

Effectively, the wavefront 3003 comprises a lens fingerprint (e.g., thelens fingerprint 3002 of tuning apparatus) and a performance fingerprintof the lens model. The performance fingerprint refers to values ofadjustments of optical elements given the lens fingerprint 3002 of thetuning apparatus. In an embodiment, the lens fingerprint 3002 may befixed, thus the adjusting of the wavefront parameter 3003 is based onthe performance fingerprint of the lens model. In an embodiment, awavefront may be represented as a combination (e.g., a summation) of thelens fingerprint and the performance fingerprint of the lens model 3001.Thereby, the adjusted wavefront 3003 includes the fixed lens fingerprintand adjustments (or corrections) corresponding to the lens fingerprintof the tuning scanner.

The process P305 involves determining a substrate pattern 3005 from theinitial wavefront 3003 (e.g., determined in a 1^(st) iteration) oradjusted wavefront 3003 (e.g., in iteration number 2, 3, 4, . . . ).Further, the process P305 involves determining the tuning performancefrom the substrate pattern. For example, the tuning performance may be acontour (e.g., 6016 of FIG. 6C) of a feature within the substratepattern 3005. In an embodiment, the tuning performance can be determinedusing image processing configured to extract information (e.g.,contours, CD, EPE, etc.) related to the tuning performance of the tuningscanner. The tuning performance can be further used to compare with thereference performance 3007 and adjust the wavefront such that the tuningperformance closely matches the reference performance 3007. An exampleof comparing reference performance is further discussed with respect toFIGS. 6A-6C.

In an embodiment, determining the substrate pattern involves simulationof a process model of the patterning process using the initial wavefrontor adjusted wavefront. The process model may include a mask modelconfigured to predict a mask image based from a mask pattern, an opticalmodel configured to predict an aerial image from the mask image, aresist model configured to predict a resist image based on the aerialimage, an etch model configured to predict an etch image based on theresist image, or a combination thereof.

In another embodiment, determining the substrate pattern involvesreceiving, via a metrology tool, substrate measurements of an exposedsubstrate, where the substrate is exposed using the wavefront 3003(e.g., wavefront 4003 in FIG. 4 ); and determining the substrate patternbased on contour extraction from the substrate measurement. In anembodiment the metrology tool may be an optical tool or an e-beammicroscope (e.g., SEM). In an embodiment, the measurement may be a SEMimage of an exposed substrate.

Process P307 involves evaluating a cost function based on the tuningperformance and the reference performance 3007. In an embodiment, thecost function is a difference between the tuning performance and thereference performance 3007. The cost function may be reduced (in anembodiment, minimized or maximized), for example, by iterativelymodifying the wavefront to produce tuning performance closer to thereference performance. In an embodiment, the cost function is an edgeplacement error, CD, an error within a tolerance band of edge placement(e.g., see FIG. 7 ). In an embodiment, the cost function is evaluated atthe evaluation points (e.g., 6008 of FIG. 6B) along the contour. In anembodiment, the EPE may be minimized or 1/EPE may be maximized.

Process P309 involves determining whether a convergence has beenreached. In an embodiment, the convergence may be based on a metricrelated to a maximum number of iterations, a threshold value related toEPE (CD, or other parameters). In an embodiment, the convergenceindicates that there is no further improvement in the tuning scannerperformance as a result of wavefront adjustments.

Process P311 involves adjusting the wavefront parameter 3110 of theinitial wavefront 3003 (e.g., 4003 in FIG. 4 ) based on a gradient ofthe cost function such that the cost function is improved. For example,the gradient may be computed as a derivative of the cost function withrespect to EPE (or CD). For example, the gradient may be a partialderivative of the cost function with respect to EPE1, EPE2, EPE3, . . .at different evaluation points along a reference contour. The gradientprovides a guidance about which EPEs should be reduced to reduce thevalue of the cost function. Accordingly, the wavefront parameters aremodified so that the resulting contour reduces the respective EPEs. Inan embodiment, EPE may be evaluated at different evaluation points atshown and discussed with respect to FIG. 6C. Thus, the adjustedwavefront includes modification of wavefront parameters at one or morelocation across (e.g., along the length) the slit. In an embodiment, theadjustment includes modifications of Zernike coefficients.

Once an optimized wavefront 3110 for the tuning scanner is determined,the method may further involve converting, via the lens model, thewavefront parameters to the actuator movements, and actuating theoptical system of the tuning apparatus based on the actuator movements.

FIG. 4 illustrates example wavefronts at different locations across aslit 4003 generated during wavefront optimization process (e.g., 3000 or8000). FIG. 4 shows a first wavefront 4003 a determined at a firstlocation (e.g., a first end of the slit), a second wavefront 4003 bdetermined at a second location (e.g., a center of the slit), a thirdwavefront 4003 c determined at a third location (e.g., a second end ofthe slit), and so on. Each of the wavefronts 4003 a-4003 c maypotentially contribute to an error (e.g., measured in EPE, CD or otherfeature related metric) in the printed pattern on a substrate. In anembodiment, the errors (e.g., EPE) are added to determine a cumulativeerror (e.g., sum of EPEs). The cumulative error may be the costfunction, which is further used to adjust a wavefront (i.e., wavefrontparameters) such that the cumulative error is reduced (in an embodiment,minimized). For example, referring to FIGS. 6A-6C, EPEs are evaluated atvarious evaluation points along a contour (e.g., extracted from asimulated pattern) of a tuning scanner and wavefront parameters such astilt and offset are determined (e.g., in process P303/P805) until theEPE is reduced or minimized (e.g., in process P309/P811). Uponconvergence, an optimized version of the wavefronts 4003 a-4003 c isobtained.

FIG. 5 is an example of an ideal performance corresponding to a scannerwith no aberrations. In an embodiment, the ideal performance isrepresented by a simulated pattern 5006 (interchangeably referred ascontour 5006). In FIG. 5 , the mask pattern 5002 is a mask pattern withoptical proximity correction corresponding to a rectangular shapeddesign pattern 5004. The mask pattern 5002 is further used to simulatethe patterning process thereby generating the simulated pattern 5006. Inan embodiment, the simulation includes a process model (e.g., includingoptical model) without aberrations contributions. The simulated contour5006 can aligned with the design pattern 5004 to determine, for example,EPE between the contour 5006 and 5004. In an embodiment, evaluationpoints 5008 may be marked along the simulated contour 5006. Theevaluation points 5008 are points along a contour used for evaluation ofparameters (e.g., CD) related to a feature or parameters (e.g., EPE).The evaluation may involve making measurements at the evaluation pointsand/or determining, for example, EPE at one or more of the evaluationpoints or a CD value (e.g., length or width of the contour 5006) atcertain location on the contour 5006. The measurements (e.g., EPE andCD) may be further used in the cost function (e.g., in process P309) tomodify the wavefront or the wavefront parameters (e.g., in processP303).

FIG. 6A illustrates an example of a reference contour 6006 overlappedwith the ideal contour 5006 of FIG. 5 . The reference contour 6006 maybe obtained via simulation or measurements of exposed wafer (e.g., fromSEM image). The reference contour 6006 accounts for aberrations of thereference apparatus, thereby contour 6006 is different from the idealcontour 5006. In an embodiment, the reference contour 6006 may beobtained via simulation of process models (e.g., mask model, opticalmodel, resist model etc.) with aberration or lens fingerprint (alsoreferred as a reference lens fingerprint) of a reference apparatus asone of the inputs to the simulation. The reference contour 6006 isoffset from the ideal contour 5006 when overlapped. In an embodiment,the reference contour 6006 may be used to determine the referenceperformance (e.g., contour, CD, etc.). Further, wavefront adjustment forthe tuning scanner may be determined based on a difference between atuning performance and the reference performance 6006.

The tuning performance refers to the performance of the tuning scanner.The tuning performance may be determined from a tuning contour 6016(shown in FIG. 6C) in a similar manner as the reference performance. Inan embodiment, the tuning performance (e.g., 6016) may be obtained viasimulation of the process models including a lens fingerprint of thetuning scanner. The simulation results in the contour 6016. In anembodiment, the lens fingerprint of the tuning scanner is fixed, whilethe wavefront parameters are varied to obtain the tuning performance(e.g., 6016) that matches the reference performance (e.g., 6006).

During the wavefront optimization process (e.g., process P303-P311 orP805-P813), the tuning contour 6016 may change depending on thewavefront parameters (e.g., in process P303) employed during simulationof the process model. For example, as the wavefront or the wavefrontparameters change, the simulation of the process model generatesdifferent tuning contours. Then, a difference of the tuning contour withrespect to the reference contour (which may be fixed) is be determined.

For example, the tuning contour 6016 may be aligned with the referencecontour 6006 (shown in FIG. 6C) and a difference between the contours6006 and 6016 may be determined. The difference may be EPE, CD, or otherparameters related to the features. In an embodiment, the differencebetween the contours 6006 and 6016 may be determined at evaluationpoints 6008, which serve similar purpose as points 5008 of FIG. 5 . Forexample, evaluation points 6008 (shown in FIG. 6B) may be marked on thereference contour 6006 and a difference (e.g., EPE, CD, etc.) betweencontours 6006 and 6016 may be determined at such points 6008.

FIG. 7 illustrates a tolerance band for a contour based matching oftuning scanner. The tolerance band refers to an upper limit and a lowerlimit of the contour (or related metric such as EPE or CD) with respectto a reference contour or an ideal contour. In FIG. 7 , an ideal contour5006 (or reference contour 6006) corresponding to the feature 5004 isused as reference and the upper limit (e.g., 7007) and a lower limit(e.g., 7005) is set around the contour 5006. In an embodiment, the upperlimit is an outer offset contour 7007 and the lower limit is an inneroffset contour 7005. The outer offset contour 7007 and the inner offsetcontour 7005 are contours obtained by offsetting the ideal contour 5006by a pre-determined distance.

Further evaluation points may be marked on the contours 7005 and 7007 todetermine whether a tuning performance (e.g., a tuning contour) iswithin the tolerance band (i.e., within the contour 7007 and 7005). Inan embodiment, during the wavefront optimization process (e.g.,processes P303-P311 or P805-P813), the wavefront parameters may bemodified until the tuning contour is contained within the toleranceband.

FIG. 8 is a flow chart of another for wavefront optimization of a tuningscanner with respect to a reference apparatus. The method involvesobtaining a reference performance (e.g., 8003 from process P803) of areference apparatus corresponding to a reference lens fingerprint 8001(e.g., using a shearing interferometer), and a lens fingerprint (e.g.,8004) of a tuning scanner. Further, the method involves determining(e.g., in process P805) a wavefront parameter of the tuning scannerbased on the lens fingerprint 8005 and a cost function, where the costfunction computes a difference between the reference performance and atuning scanner performance. The reference performance and the tuningperformance (e.g., contours of FIGS. 6B-6C) are similar to thatdiscussed with respect to FIG. 3 .

According to an embodiment, the determining of the wavefront parameteris an iterative process (e.g., involving process P805, P807, P809, P811,and/or P813). An iteration includes determining, via simulation of theprocess model, a substrate pattern (e.g., 8005) using a patterningdevice pattern (e.g., a through-slit mask 8002) and a lens fingerprint(8007) of the tuning scanner, determining the tuning scanner performancebased on the substrate pattern (e.g., 8008), followed by evaluating(e.g., process P809) the cost function based on the tuning scannerperformance and the reference performance, and adjusting (e.g., processP813) the wavefront parameter based on a gradient of the cost functionwith respect to the wavefront parameter, such that the cost function isimproved. The different process involved in the method 8000 are furtherdiscussed in detail below.

Process P801 involves obtaining a reference performance 8001 of thereference apparatus, a patterning device pattern (e.g., a through-slitmask), and a lens fingerprint 8005 of a tuning scanner. In anembodiment, a “through-slit mask” is post OPC mask for specific slitpositions (e.g., along a length of a slit) to compensate for theproximity and shadow effect which varies thru-slit.

In an embodiment, a through-slit mask (e.g., 8002) is generated viasimulation of a phase control source mask optimization process, where alens aberration model is included in the source mask optimization (SMO)process. The SMO is an illumination mode and patterning device patternoptimization method that allows for simultaneous optimization of theillumination mode and the patterning device pattern using an objectivefunction without constraints and within a practicable amount of time isdescribed in PCT Patent Application Publication No. WO 2010/059954,titled “Fast Freeform Source and Mask Co-Optimization Method”, which ishereby incorporated by reference in its entirety. Another illuminationand patterning device optimization method and system that involvesoptimizing the illumination by adjusting pixels of the illuminationdistribution is described in U.S. Patent Application Publication No.2010/0315614, titled “Source-Mask Optimization in LithographicApparatus”, which is hereby incorporated by reference in its entirety.

In an embodiment, when a light propagating through-slit is passed overpatterning device pattern 8002 (e.g., a mask pattern or a through-slitmask) and the optical system, a substrate pattern of desired layout ordesign layout is printed on the substrate. The printed pattern is afunction of the wavefront generated by a patterning apparatus (e.g., areference apparatus or the tuning scanner). As mentioned earlier, thewavefront is a function of characteristics (e.g., aberrations) of theoptical system. Thus, depending on the lens fingerprints (e.g., 8001 and8007) a scanner may produce different patterns/performance.

In an embodiment, the reference performance (e.g., 6006) may be obtainedvia measurements on a wafer printed on a reference apparatus or viasimulation of process model configured to predict reference performance.

For example, in process P803, the reference performance is determined bymeasuring the reference lens fingerprint 8001 of the referenceapparatus, generating, via simulation of a process model, a referencepattern based on the measured lens fingerprint of the referenceapparatus and a through-slit mask corresponding to a design layout, anddetermining the reference performance 8003 based on a contour of thereference pattern (e.g., as discussed earlier with respect to FIGS. 5,6A-6C and 7 ).

In an embodiment, the reference apparatus may be a scanner of a waferfabrication facility, an ideal scanner having no optical aberrations;and/or an aberration compensated scanner that is compensated for averageaberration of a plurality of scanners within the wafer fabricationfacility.

Process P805 (similar to P305) involves determining a wavefrontparameter of the tuning scanner. For example, as discussed in P305, thewavefront parameter may be tilt, offset, and/or curvature of thewavefront. In an embodiment, the wavefront may be expressed as Zernikepolynomial and the wavefront parameters are the Zernike coefficients.

Process P807 involves determining via simulation of the process model,the substrate pattern 8008 using a patterning device pattern, and thelens fingerprint 8007 of the tuning scanner, and determining the tuningscanner performance (e.g., 6016) based on the substrate pattern 8008(interchangeably referred as performance 8008). As mentioned earlier,the process model may be a mask model, optical model, resist model, or acombination thereof.

Process P809 (similar to P307) involves evaluating the cost functionbased on the tuning scanner performance 8008 and the referenceperformance 8003. For example, the cost function may be a differencebetween the performances. In an embodiment, the cost function is an edgeplacement error, CD and/or an error within a tolerance band of edgeplacement.

Process P811 involves determining whether a convergence has beenreached. Similar to process P309, for example, the convergence may bebased on a metric related to a maximum number of iterations, a thresholdvalue related to EPE (CD, or other parameters). In an embodiment, theconvergence indicates that there is no further improvement in the tuningscanner performance as a result of wavefront adjustments.

Process P813 involves adjusting the wavefront parameter 8110 based on agradient of the cost function with respect to the wavefront parameter,such that the cost function is improved. Similar to process P311 anddiscussed in FIG. 6C, for example, the gradient may be computed as aderivative of the cost function with respect to with respect to EPE (orCD). In an embodiment, the adjustment includes modifications of Zernikecoefficients.

FIG. 9 is a flow chart of a method for determining wavefront based onhot spot patterns. For example, the tuning scanner performance may beevaluated with respect to hot spot patterns, over different periods oftime during the patterning process to ensure a consistent performance ofthe tuning scanner. In an embodiment, the evaluation may involvecomparison with reference performance stored in a database. The databaseincludes previously determined optimized wavefront parameters for one ormore (in an embodiment, each) hot spot pattern. Based on the comparisonwith the reference performance, a set of wavefront parameters may beselected to adjust the tuning scanner.

Process P901 involves obtaining a plurality of hot spot patternscorresponding to a layer of a substrate, a plurality of wavefronts 9001(e.g., obtained from methods 3000 or 4000) corresponding to theplurality of hot spot patterns, and a lens fingerprint (e.g., 3002,8007, etc.) of a tuning scanner. An example method of obtaining hot spotpatterns is discussed in FIG. 11

In an embodiment, one or more of the plurality of wavefronts includeoptimized wavefront parameters (e.g., 3110 or 8110). Furthermore, theone or more of the plurality of wavefronts is associated with aparticular reference performance. Such relational information related tothe hot spot patterns and the reference performance can be stored in adatabase (e.g., a database 152 of FIG. 20 ) and retrieved to tune ascanner. In an embodiment, the tuning may be offline or real-time, forexample, during a manufacturing process.

Process P903 (similar to processes P807) involves determining, viasimulation of a patterning process using the lens fingerprint, a tuningscanner performance. An example of the simulation process is discussedin FIG. 10 . Further, process P905 involves selecting, via a processor(e.g., processor 104 of FIG. 20 ) wavefront parameters for the tuningscanner from the plurality of wavefronts based on comparison between thetuning scanner performance and a reference performance.

For example, if the tuning performance substantially deviates from thereference performance, then the reference performance that matches thetuning scanner performance may be retrieved from the database 152 andthe corresponding optimized wavefront parameters may be used as for thetuning scanner.

The above methods of wavefront optimization to achieve consistency inpatterning process enable chipmaker to improve scanner to scannerperformance matching, e.g., EPE and or CD through slit matching. Thematching process eliminate the time consuming lens setup procedure andscanner down time for a specific technology node and layer. Also, withabove methods, the productivity can be improved in real-time. Thus, theproductivity is not dedicated to reticle and/or scanner improvement.

An exemplary flow chart for modeling and/or simulating parts of apatterning process (e.g., lithography in a lithographic apparatus) isillustrated in FIG. 10 . As will be appreciated, the models mayrepresent a different patterning process and need not comprise all themodels described below. A source model 600 represents opticalcharacteristics (including radiation intensity distribution, bandwidthand/or phase distribution) of the illumination of a patterning device.The source model 600 can represent the optical characteristics of theillumination that include, but not limited to, numerical aperturesettings, illumination sigma (σ) settings as well as any particularillumination shape (e.g. off-axis radiation shape such as annular,quadrupole, dipole, etc.), where σ (or sigma) is outer radial extent ofthe illuminator.

A projection optics model 610 represents optical characteristics(including changes to the radiation intensity distribution and/or thephase distribution caused by the projection optics) of the projectionoptics. The projection optics model 610 can represent the opticalcharacteristics of the projection optics, including aberration,distortion, one or more refractive indexes, one or more physical sizes,one or more physical dimensions, etc.

The patterning device model module 120 captures how the design featuresare laid out in the pattern of the patterning device and may include arepresentation of detailed physical properties of the patterning device,as described, for example, in U.S. Pat. No. 7,587,704. The objective ofthe simulation is to accurately predict, for example, edge placementsand CDs, which can then be compared against the device design. Thedevice design is generally defined as the pre-OPC patterning devicelayout, and will be provided in a standardized digital file format suchas GDSII or OASIS.

A design layout model 620 represents optical characteristics (includingchanges to the radiation intensity distribution and/or the phasedistribution caused by a given design layout) of a design layout (e.g.,a device design layout corresponding to a feature of an integratedcircuit, a memory, an electronic device, etc.), which is therepresentation of an arrangement of features on or formed by thepatterning device. The design layout model 620 can represent one or morephysical properties of a physical patterning device, as described, forexample, in U.S. Pat. No. 7,587,704, which is incorporated by referencein its entirety. Since the patterning device used in the lithographicprojection apparatus can be changed, it is desirable to separate theoptical properties of the patterning device from the optical propertiesof the rest of the lithographic projection apparatus including at leastthe illumination and the projection optics.

An aerial image 630 can be simulated from the source model 600, theprojection optics model 610 and the design layout model 620. An aerialimage (AI) is the radiation intensity distribution at substrate level.Optical properties of the lithographic projection apparatus (e.g.,properties of the illumination, the patterning device and the projectionoptics) dictate the aerial image.

A resist layer on a substrate is exposed by the aerial image and theaerial image is transferred to the resist layer as a latent “resistimage” (RI) therein. The resist image (RI) can be defined as a spatialdistribution of solubility of the resist in the resist layer. A resistimage 650 can be simulated from the aerial image 630 using a resistmodel 640. The resist model can be used to calculate the resist imagefrom the aerial image, an example of which can be found in U.S. PatentApplication Publication No. US 2009-0157360, the disclosure of which ishereby incorporated by reference in its entirety. The resist modeltypically describes the effects of chemical processes which occur duringresist exposure, post exposure bake (PEB) and development, in order topredict, for example, contours of resist features formed on thesubstrate and so it typically related only to such properties of theresist layer (e.g., effects of chemical processes which occur duringexposure, post-exposure bake and development). In an embodiment, theoptical properties of the resist layer, e.g., refractive index, filmthickness, propagation and polarization effects—may be captured as partof the projection optics model 610.

So, in general, the connection between the optical and the resist modelis a simulated aerial image intensity within the resist layer, whicharises from the projection of radiation onto the substrate, refractionat the resist interface and multiple reflections in the resist filmstack. The radiation intensity distribution (aerial image intensity) isturned into a latent “resist image” by absorption of incident energy,which is further modified by diffusion processes and various loadingeffects. Efficient simulation methods that are fast enough for full-chipapplications approximate the realistic 3-dimensional intensitydistribution in the resist stack by a 2-dimensional aerial (and resist)image.

In an embodiment, the resist image can be used an input to apost-pattern transfer process model module 150. The post-patterntransfer process model 150 defines performance of one or morepost-resist development processes (e.g., etch, development, etc.).

Simulation of the patterning process can, for example, predict contours,CDs, edge placement (e.g., edge placement error), etc. in the resistand/or etched image. Thus, the objective of the simulation is toaccurately predict, for example, edge placement, and/or aerial imageintensity slope, and/or CD, etc. of the printed pattern. These valuescan be compared against an intended design to, e.g., correct thepatterning process, identify where a defect is predicted to occur, etc.The intended design is generally defined as a pre-OPC design layoutwhich can be provided in a standardized digital file format such asGDSII or OASIS or other file format.

Thus, the model formulation describes most, if not all, of the knownphysics and chemistry of the overall process, and each of the modelparameters desirably corresponds to a distinct physical or chemicaleffect. The model formulation thus sets an upper bound on how well themodel can be used to simulate the overall manufacturing process.

Inspection of, e.g., semiconductor wafers is often done withoptics-based sub-resolution tools (bright-field inspection). But, insome cases, certain features to be measured are too small to beeffectively measured using bright-field inspection. For example,bright-field inspection of defects in features of a semiconductor devicecan be challenging. Moreover, as time progresses, features that arebeing made using patterning processes (e.g., semiconductor features madeusing lithography) are becoming smaller and in many cases, the densityof features is also increasing. Accordingly, a higher resolutioninspection technique is used and desired. An example inspectiontechnique is electron beam inspection. Electron beam inspection involvesfocusing a beam of electrons on a small spot on the substrate to beinspected. An image is formed by providing relative movement between thebeam and the substrate (hereinafter referred to as scanning the electronbeam) over the area of the substrate inspected and collecting secondaryand/or backscattered electrons with an electron detector. The image datais then processed to, for example, identify defects.

So, in an embodiment, the inspection apparatus may be an electron beaminspection apparatus (e.g., the same as or similar to a scanningelectron microscope (SEM)) that yields an image of a structure (e.g.,some or all the structure of a device, such as an integrated circuit)exposed or transferred on the substrate.

FIG. 11 shows a flow chart for a method of determining existence ofdefects in a lithography process, according to an embodiment. In processP411, hot spots or locations thereof are identified using any suitablemethod from patterns (e.g., patterns on a patterning device). Forexample, hot spots may be identified by analyzing patterns on patternsusing an empirical model or a computational model. In an empiricalmodel, images (e.g., resist image, optical image, etch image) of thepatterns are not simulated; instead, the empirical model predictsdefects or probability of defects based on correlations betweenprocessing parameters, parameters of the patterns, and the defects. Forexample, an empirical model may be a classification model or a databaseof patterns prone to defects. In a computational model, a portion or acharacteristic of the images is calculated or simulated, and defects areidentified based on the portion or the characteristic. For example, aline pull back defect may be identified by finding a line end too faraway from its desired location; a bridging defect may be identified byfinding a location where two lines undesirably join; an overlappingdefect may be identified by finding two features on separate layersundesirably overlap or undesirably not overlap. An empirical model isusually less computationally expensive than a computational model. It ispossible to determine and/or compile process windows of the hot spotsinto a map, based on hotspot locations and process windows of individualhot spots—i.e. determine process windows as a function of location. Thisprocess window map may characterize the layout-specific sensitivitiesand processing margins of the patterns. In another example, the hotspots, their locations, and/or their process windows may be determinedexperimentally, such as by FEM wafer inspection or a suitable metrologytool. The defects may include those defects that cannot be detected inan after-development-inspection (ADI) (usually optical inspection), suchas resist top loss, resist undercut, etc. Conventional inspection onlyreveals such defects after the substrate is irreversibly processed(e.g., etched), at which point the wafer cannot be reworked. So, suchresist top loss defects cannot be detected using the current opticaltechnology at the time of drafting this document. However, simulationmay be used to determine where resist top loss may occur and what theseverity would be. Based on this information, it may be either decidedto inspect the specific possible defect using a more accurate inspectionmethod (and typically more time consuming) to determine whether thedefect needs rework, or it may be decided to rework the imaging of thespecific resist layer (remove the resist layer having the resist toploss defect and recoat the wafer to redo the imaging of the specificlayer) before the irreversible processing (e.g., etching) is done.

In process P412, processing parameters under which the hot spots areprocessed (e.g., imaged or etched onto a substrate) are determined. Theprocessing parameters may be local—dependent on the locations of the hotspots, the dies, or both. The processing parameters may beglobal—independent of the locations of the hot spots and the dies. Oneexemplary way to determine the processing parameters is to determine thestatus of the lithographic apparatus. For example, laser bandwidth,focus, dose, source parameters, projection optics parameters, and thespatial or temporal variations of these parameters, may be measured fromthe lithographic apparatus. Another exemplary way is to infer theprocessing parameters from data obtained from metrology performed on thesubstrate, or from operator of the processing apparatus. For example,metrology may include inspecting a substrate using a diffractive tool(e.g., ASML YieldStar), an electron microscope, or other suitableinspection tools. It is possible to obtain processing parameters for anylocation on a processed substrate, including the identified hot spots.The processing parameters may be compiled into a map—lithographicparameters, or process conditions, as a function of location. Of course,other processing parameters may be represented as functions of location,i.e., a map. In an embodiment, the processing parameters may bedetermined before, and preferably immediately before processing eachhotspot.

In process P413, existence, probability of existence, characteristics,or a combination thereof, of a defect at a hot spot is determined usingthe processing parameters under which the hot spot is processed. Thisdetermination may be simply comparing the processing parameters and theprocess window of the hot spot—if the processing parameters fall withinthe process window, no defect exists; if the processing parameters falloutside the process window, at least one defect will be expected toexist. This determination may also be done using a suitable empiricalmodel (including a statistical model). For example, a classificationmodel may be used to provide a probability of existence of a defect.Another way to make this determination is to use a computational modelto simulate an image or expected patterning contours of the hot spotunder the processing parameters and measure the image or contourparameters. In an embodiment, the processing parameters may bedetermined immediately (i.e., before processing the pattern or the nextsubstrate) after processing a pattern or a substrate. The determinedexistence and/or characteristics of a defect may serve as a basis for adecision of disposition: rework or acceptance. In an embodiment, theprocessing parameters may be used to calculate moving averages of thelithographic parameters. Moving averages are useful to capture long termdrifts of the lithographic parameters, without distraction by short termfluctuations.

In an embodiment, hot spots are detected based on the simulated image ofpattern on a substrate. Once the simulation of the patterning process(e.g., including process models such OPC and manufacturability check) iscomplete, potential weak points, i.e., hot spots, in the design as afunction of process conditions may be computed according to one or moredefinitions (e.g., certain rules, thresholds, or metrics). Hot spots maybe determined based on absolute CD values, on the rate of change of CDvs. one or more of the parameters that were varied in the simulation(“CD sensitivity”), on the slope of the aerial image intensity, or onNILS (i.e., “edge slope,” or “normalized image log slope,” oftenabbreviated as “NILS.” Indicating lack of sharpness or image blur) wherethe edge of the resist feature is expected (computed from a simplethreshold/bias model or a more complete resist model). Alternatively,hot spots may be determined based on a set of predetermined rules suchas those used in a design rule checking system, including, but notlimited to, line-end pullback, corner rounding, proximity to neighboringfeatures, pattern necking or pinching, and other metrics of patterndeformation relative to the desired pattern. The CD sensitivity to smallchanges in mask CD is a particularly important lithographic parameterknown as MEF (Mask Error Factor) or MEEF (Mask Error EnhancementFactor). Computation of MEF vs. focus and exposure provides a criticalmetric of the probability that mask process variation convolved withwafer process variation will result in unacceptable pattern degradationof a particular pattern element. Hot spots can also be identified basedon variation in overlay errors relative to underlying or subsequentprocess layers and CD variation or by sensitivity to variations inoverlay and/or CD between exposures in a multiple-exposure process.

A wavefront offset solution configured to optimize performance per layerand per scanner via compensating for Lens FingerPrint (LFP) offset. LFPrefers to a lens aberration specific to a scanner being tuned. In anembodiment, the wavefront offset solution involves pupil optimization(e.g., FIG. 12A), where a pupil is determined based on aberrationcharacteristics of a lens. The pupil optimization may be performed tominimize layer's sensitivity to aberration that are actually present ina scanner. For example, the pupil 1210 is optimized to generate anoptimized pupil 1220. Further the solution may involve wavefrontoptimization based on the LFP of the scanner. For example, FIG. 12Billustrates example LFP 1250 of the to-be-tuned scanner used to generatean optimized wavefront 1260. The LFP 1250 of the scanner includesaberrations in pupil areas 1251 and 1252. As discussed earlier, thewavefront optimization is based on matching a wavefront (e.g., 1260)with a reference wavefront (e.g., an ideal wavefront). However, the LFPbased wavefront optimization is specific to a particular scanner. Thesolution compensates for aberrations in layer sensitive pupil areas. Inan addition, the solution is limited to lens correction potential of thescanner.

The Wavefront Offset solution does not consider mirror heatingtransient. The mirror heating transient refers to lens aberrations orchanges to lens aberrations caused due to heating of mirrors of the lensduring imaging of a substrate via a patterning apparatus. In anembodiment, one or more patterns may be more sensitive to the mirrorheating transient than other patterns.

Thus, the Wavefront Offset solution has several limitation compared to aLithographic metric solution. For example, the limitations include, butnot limited to: (i) optimize for static aberration components (LFP, MHsaturation), but not for dynamic aberration components (MH transients,intra lot mirror drift); (ii) the solution requires a correction recipeper scanner rather than the same recipe for all scanner; (iii) thesolution requires a regular update of the correction recipe if thescanner lens calibration has been updated or if the LFP drifts. As aresult a regular monitoring may be desired for re-optimization; and (iv)the optimization is based on through slit variation.

The present methods (e.g., 1300 and 1800) provide a lithographic metricbased solution for optimizing of the performance of all scanners. On theother hand, the wavefront offset solution determines wavefrontadjustment parameters per scanner based on a reference or idealwavefront and a scanner specific LFP. Such LFP based optimization maynot be determine wavefront parameters applicable to other scanners inthe substrate manufacturing process.

In an embodiment, a lithographic metric is associated with a layerspecific optimization of the merit function of the Lens model (DLM) usedduring lot control. Example of lithographic metric is a function of EPEand a pattern placement error (PPE), further discussed in a method 1300of FIG. 13 detail below. In an embodiment, the lithographic metric is afunction of sensitivity of a lens knob setting to a residual aberrationwavefront and measured wavefront, further discussed in method 1800 ofFIG. 18 .

FIG. 13A describes a method 1300 for determining a lens adjustmentparameter value for a patterning apparatus used in a patterning process.In an embodiment, the method 1300 is an optimization process where thegoal is not to optimize scanner-to-scanner performance based on e.g., CDmatching, rather the method 1300 optimizes an overlay, EPE or defectperformance of any scanner of the chip manufacturing unit. Further, themethod 1300 does not necessarily optimize a wavefront, rather the methodoptimizes a lithographic metric (e.g., a function of EPE and PPE).Furthermore, the method 1300 can be extended to be used with optimizingone or more aspects (e.g., SMO or process window) of the patterningprocess. For example, the SMO process may be tuned based on thelithographic metric so that a ratio of CD to PPE is within a desiredrange.

According to present disclosure, using the method 1300 with SMO canimprove on-product overlay performance in two ways. First, the method1300 enables reducing odd Zernike (e.g. Z7) sensitivity that will reducea feature dependent overlay contribution to the on-product overlaybudget. Secondly, deweighing non-relevant areas (e.g., associated withZ7) of the illumination pupil gives the lens model more correctioncapability for relevant Zernike components (e.g., associated with highercorrection potential of a scanner). For example, including the slitorders of Z2 and Z3, which are directly associated with overlaycorrection capability. The method 1300 employing a pupil weight map anda lithographic metric to obtain lens adjustment parameters is furtherexplained with procedures P1301, 1303 as follows

Procedure P1301 involves obtaining (i) a pupil weight map associatedwith an exposure wavefront, wherein weights of the pupil weight map areassociated with a performance metric of the patterning apparatus, and(ii) a lens model of a patterning apparatus, the lens model configuredto convert an aberration wavefront parameter associated with theexposure wavefront to a lens adjustment parameter.

In an embodiment, the exposure wavefront is a through-slit wavefront.The slit has a rectangular shape. In an embodiment, the slit field has acurved shape.

In an embodiment, the lens model 1301 includes constraints related tocorrection limitations of the patterning apparatus corresponding to thegiven radiation wavefront. For example, as discussed earlier, certainaberrations related to an optical system may be correctable via lensadjustments associated with, e.g., lower order Zernikes (e.g., Z1-Z5),while some aberrations associated with e.g., higher order Zernikes(e.g., Z10, Z24, Z30, etc.) are not correctable. In an embodiment, thewavefront may be presented by, for example, a combination of Zernikepolynomials and the higher order Zernikes may be correctable via arelated lower order Zernikes. In an embodiment, the combination ofZernike polynomials that explain most aberrations may be obtained via aprincipal component analysis (PCA). Each principal component identifiedby the PCA may represent a different wavefront. In an embodiment, suchPCA may be used to determine a pupil weight map 1302.

In an embodiment, the pupil weight map 1302 is a pixelated image,wherein a given pixel of the pixelated image is assigned a weight basedon an impact of change in the given pixel value on the performancemetric (e.g., including EPE and PPE). The weights of the pupil weightmap 1302 may be assigned in several ways, including but not limited to,diffraction orders, a linear combination of Zernike polynomials,principal component analysis (PCA) a set of wavefront associated withdifferent scanners, a mini-batch algorithm (where wavefront data fromdifferent scanners is split into batches and used to update weight map),or other appropriate parameters associated with the aberrationwavefront. In an embodiment, the mini-batch data is associated withdifferent setting (e.g., dose, focus) used to image a substrate.

In an embodiment, the weights of the pupil weight map are based ondiffraction information associated with an illumination pupil, where thediffraction information comprises diffraction orders and/or diffractionintensity pattern. In an embodiment, a portion of the pupil weight mapassociated with a diffraction order is assigned a weight 1 and anotherportion not associated with the diffraction order is assigned a weight0.

An example of such pupil weight map based on a dipole pupil isillustrated in FIG. 14 . A pupil weight map 1400 (an example of map1302) comprises weights 1 assigned to portions 1401, 1402 and 1402associated with a corresponding (similar) pupil shape. Furthermore,portions 1411 and 1412 includes weights 0. In an embodiment, the pupilweight map 1400 is used as a lithographic metric. Thus, during anoptimization process (e.g., SMO or patterning process windowoptimization, etc.), wavefronts (e.g., represented by Zernikepolynomials) associated with such portions 1401, 1402, 1403 are assignedhigher weights to generate an improved output (e.g., mask pattern,process window etc.) compared to existing approaches. In an embodiment,the pupil shape refers to portions of the pupil that are illuminated soas to compensate for particular aberrations of a lens. It can beunderstood that the pupil weight map 1400 is an example and the weightsare not limited to weights 0 and 1.

FIGS. 15A and 15B illustrate another example of generating a pupilweight map based on illumination pattern. In FIG. 15A, an illuminationpattern 1510 comprising diffraction orders in portions 1511 and 1512,and no diffraction orders in the remaining locations associated with anillumination pupil. Based on such illumination pattern 1510, anaberration wavefront 1520 (in FIG. 15B) is generated. Then, according topresent disclosure, locations 1521 and 1522 of the wavefront associatedwith the diffraction orders (e.g., portions locations 1511 and 1512 inFIG. 15A) are assigned relatively higher weights compared to locationsassociated with the no diffractions. In an embodiment, the weights maybe a positive real number (e.g., 0, 0.1, 0.2, 0.3, 0.4, 1, 2, etc.) or apositive integer (e.g., 1).

As mentioned earlier, different scanners may generate differentwavefronts. For example, referring to FIG. 16A-16C, an illuminationpattern 1600 comprising diffraction orders at locations (or portions)1601 and 1602 of a pupil may result in a first wavefront 1610 on a firstscanner and a second wavefront 1620 on a second scanner. Regardless, thepupil weight map (e.g., 1302) will assign weights to wavefronts in asimilar manner. For example, a wavefront portion associated withlocations 1601 and 1602 will be assigned higher weight relative to otherlocations (or portions) of the wavefront (e.g., 1610 and 1620). Hence,even if the wavefronts 1610 and 1620 do not particularly match areference or ideal wavefront, appropriate lens adjustments may bedetermined for each scanner.

In an embodiment, the diffraction intensity pattern is a linearcombination of Zernike polynomials describing the weight. In anembodiment, the weights of the pupil weight map are based on Zernikesensitivities, a given Zernike sensitivity being a partial derivative ofthe performance metric with respect to a given Zernike polynomial. Forexample, partial derivative of a SMO merit function (e.g., Eq 1discussed later in the disclosure) with respect to the Zernikepolynomial.

In an embodiment, a combination of Zernike polynomials are obtained viaPCA. In an embodiment, the pupil weight map may be a PCA component ormay be derived from a sum of each of the PCA component. For example,FIG. 17 illustrates example PCA components P1-P17 that explain most ofthe variations in imaging performance related to wavefronts and/oraberrations. Then, a pupil weight map may be a PCA component P1, P2, orany other PCA component, or a sum of PCAs P1-P17.

In an embodiment, the weights of the pupil weight map are based onprincipal component analysis (PCA) of a set of wavefronts, the set ofwavefronts obtained from one or more scanners used in the patterningprocess. In an embodiment, the weights of the pupil weight map are basedon a sensitivity of a principal component of a set of wavefrontsdetermined with respect to the performance metric.

Thus, during an optimization process (e.g., employing DLM), relevantportions of the wavefront (e.g., pixels having relatively higher impacton the performance metric) are assigned higher importance allowing thedetermination of lens adjustments or corrections to compensate foreffects due to relevant wavefront portions. Such lens adjustmentsfurther improve the imaging performance (e.g., minimum defects, betterEPE, overlay performance, etc.). Hence, even if a given wavefront of anyscanner does not match or closely match an ideal wavefront, the scannerperformance can still be improved to effectively meet the performancespecification (e.g., EPE and overlay).

Furthermore, the diffraction pattern may change during patterningprocess due to various reasons such as heat transient, drift, etc. Thechanged diffraction pattern will be reflected in the pupil weight map1302, thereby the determined lens adjustments will automaticallycompensate for dynamic changes in diffraction pattern.

In earlier discussed embodiments related to the wavefront offsetsolution, the pupil weight map (e.g., 1302, 1400, etc.) are not used.Instead, the wavefront offset solution modifies the wavefront 1520 toclosely match a reference wavefront (not shown) of a reference scanner.For example, a center and/or edge of the wavefront 1520 may be modifiedto match the reference wavefront, which will result in matchingperformance of the reference apparatus. Thus, establishing a consistentimaging performance between different scanners used in a chipmanufacturing.

Procedure P1303 involves determining, via executing the lens model 1301using the pupil weight map 1302 and the exposure wavefront, a lensadjustment parameter value 1303 such that a lens merit function (e.g.,Eq. 2 including a lithographic metric discussed later in the disclosure)associated with the lens model is improved (in an embodiment,minimized). In an embodiment, the lens metric function is a function ofthe pupil weight map 1302 (herein implemented as the lithographicmetric). It is via such lithographic metric, dynamic conditions (e.g.,changes in aberration, heat transient, etc.) associated with theaberration wavefront can be accounted for during the patterning processadjustments. Comparatively, the wavefront offset solution (e.g., LFPbased wavefront matching to a reference wavefront) is a static approachand may not account for the dynamic conditions.

In an embodiment, the aberration wavefront parameter are associated withan offset, a tilt, a curvature, and/or up to and including 3^(rd) orderor higher order parameters associated with Zernike polynomials. Then,determined the adjustment parameter values are values associated withoffset, tilt, curvature, etc.

In an embodiment, the procedure P1303 of the determining of the lensadjustment parameter is an iterative process. An example of theiterative process involves procedures P1311-P1319 illustrated in FIG.13B.

Procedure P1311 involves executing the lens model 1301 using, as input,the pupil weight map 1302 and the given exposure wavefront to generatethe aberration wavefront.

Procedure P1313 involves determining, based on the aberration wavefront,the edge placement error and the pattern placement error associated withone or more portions of the aberration wavefront. In an embodiment, thepattern placement error is a mutual shift of features in a layer, themutual shift being relative to a design layout associated with thesubstrate. For example, one or more contact holes are shifted to leftwith respect to a reference position (e.g., associated with a designlayout) on the substrate

In an embodiment, the aberration wavefront is used in a patterningprocess simulation to determine a substrate pattern. In an embodiment,the substrate pattern may be a printed pattern on the substrate imagedusing the aberration wavefront. In an embodiment, the EPE is determinedbased on edge placement gauges (or measurement locations) placed along acontour of the substrate pattern and measuring a distance between an EPgauge and a reference contour or a reference point. In an embodiment,the distance may be measured along cut lines drawn in a normal directionto the contour. Further, the PPE may be determined based on a locationof the substrate pattern with respect to a desired location or referencelocation. In an embodiment, the reference location refers to location ofanother substrate pattern on a different layer.

Procedure P1315 involves evaluating the performance metric using theedge placement error and the pattern placement error. In an embodiment,the performance metric is associated with sensitivity of the aberrationwavefront which eventually results in EPE and PPE.

In an embodiment, the performance metric (e.g., merit function of eq.1below) is a function of higher order (e.g., at least 2^(nd) order, the2^(nd) order is also known as a root mean square) of the edge placementerror and/or e.g., at least 2^(nd) order of the pattern placement error.In embodiment, the higher order (e.g., fourth order) of EPE and PPEstresses weaker points (e.g., resulting in defects). In an equationbelow, the co-efficient “c” and “PPE” help balance EPE against overlayassociated with a desired pattern to be printed on the substrate.

$\begin{matrix}{{{Merit}{function}} = {{\sum\limits_{cutlines}{\underset{dose}{\sum\limits_{Focus}}{EPE}^{4}}} + {c \cdot {PPE}^{4}}}} & \left( {{Eq}.1} \right)\end{matrix}$

Procedure P1317 involves adjusting, via lens actuator adjustment, theaberration wavefront parameter based on a gradient of the performancemetric such that the performance metric is improved. For example, thegradient may be d(merit function)/d(lens adjustment parameter) and lensadjustments may be determined such that the gradient guides the costfunction to be minimized. In an embodiment, the lens adjustment is suchthat the lithographic metric associated with DLM is minimized.

Procedure P1319 involves determining whether the merit function isreduced (in an embodiment, minimized). If not reduced, the procedurecontinues the simulation of DLM e.g., at procedure P1311. In anembodiment, once the merit function is minimized, the procedure P1303ends and the determined lens adjustment parameters values can be furtherused in the patterning process. As mentioned earlier, the lensadjustment parameters and values thereof are associated with an offset,a tilt and/or a curvature of the aberration patterns.

Procedure P1305 involves adjusting, via a patterning process simulationusing the aberration wavefront associated with the lens adjustmentparameter value, the weights of the pupil weight map such that theperformance metric is improved, the performance metric being a functionof an edge placement error and a pattern placement error associated witha desired pattern to be printed on a substrate.

The adjusted weights 1305 and associated aberration wavefront can befurther converted to lens adjustments. For example, the method 1300 mayfurther comprise procedure P1307 that involves converting, via the lensmodel 1301, the wavefront parameters (e.g., obtained in procedure P1317or P1305) to the lens adjustment parameter values 1303. Further,procedure P1309 involves actuating the optical system of a patterningapparatus based on the lens adjustment parameter values 1303.

Furthermore, the method 1300 may further include deweighting orupweighting (e.g., decreasing or increasing pixel values of the givenaberration wavefront) a region of the illumination pupil via the pupilweight map 1302; executing the lens model 1301 using the deweightedpupil weight map or the upweighted pupil weight map; and determininganother lens adjustment parameter values associated with an opticalsystem of the patterning apparatus using the deweighted pupil map andthe exposure wavefront associated therewith so that the performancemetric is minimized. In an embodiment, the deweighted region isassociated with the aberration wavefront that is correctable via awavefront manipulator of the patterning apparatus during the patterningprocess.

FIG. 18 describes a method 1800 for determining lens adjustments for apatterning apparatus. In an embodiment, the lens adjustment is asub-space of a lens knob space. In an embodiment, the lens knob spacerefers to the degrees of freedom (e.g., orientations of an array ofmirrors) associated with projection system of the patterning apparatus.In an embodiment, an aberration correction is in the space of lens knobcorrections, which represent some linear combinations of Zernikes usedin the lens model (also referred as a lens model (DLM)). In anembodiment, the impact evaluation associated with the lens knobcorrection may contain impact from (higher order) Zernikes not containedin the lens model, but affected by the lens knob. In an embodiment, suchlens adjustment is determined based on a lithographic metric configuredto drive the optimization process to a wavefront target. The method 1800is further discussed in detail below.

Procedure P1801 involves obtaining a lens merit function associated withthe lens model of the patterning apparatus and a wavefront target 1802.The wavefront target 1802 refers to a quality value or a reference valueassigned to a residual aberration wavefront associated with thepatterning apparatus. The wavefront target acts as a guide to determinea sub-space from the lens knob space. The lens knob space is a spaceassociated with degrees of freedom (DOF) of a lens of the patterningprocess. For example, a lens knob space may include 36 degrees offreedom associated with different orientation (e.g., tilt, curvature,rotation, etc.) of an array of mirrors. In an embodiment, potentialorientations such as the tilt, curvature, rotation, etc. are alsoreferred as the lens adjustment parameters.

In an embodiment, the lens merit function is determined based on alithographic merit function (e.g., Eq. 1) associated with an aspect(e.g., SMO) of the patterning process. In an embodiment, thelithographic merit function includes an edge placement error (EPE)associated with a pattern to be imaged on a substrate; and a patternplacement error (PPE). The pattern placement error being a mutual shiftof features in a layer, the mutual shift being relative to a referenceposition associated with the substrate.

In an embodiment, the lithographic merit function associated with theSMO and/or the DLM is a mountain-like landscape of lithographic meritfunction values determined with respect to parameters of a patterningprocess (e.g., dose, focus, DOF of the lens, etc.).

The mountain landscape may have several minima points (e.g., localminima and global minima) that represent minimum value around aparticular region of the landscape. In an embodiment, the global minimumof the merit function may be outside an origin associated with the lensknob space, for example global minima associated with mask 3D offsets.Then, it may be desired to direct the DLM to a desired working point(e.g., a minimum value of lithographic metric) associated with the lensknob space. Note that in lens knob space the correction capability is inprinciple 100% (full correction, no parasitic effects). In the presentdisclosure, directing of the lens model to the desired point can be doneper scanner (per point in time) through a Wavefront Offset, but due to100% correctability the same can be done through a Wavefront target 1802for all scanners (and at any point time). In an embodiment, the desiredworking point is associated with one or more points at or around theglobal minima of the lithographic merit function.

Further, procedure P1803 involves determining, via a lens model 1801 ofthe patterning apparatus using the lens merit function and wavefronttarget 1302 (e.g., the quality value associated with the residualwavefront), the lens knob setting 1803 from the lens knob space of thepatterning apparatus based on minimizing the lens merit function, thelens merit function comprising a lithographic metric associated with theresidual aberration wavefront. In an embodiment, the lens merit functionis determined based on a lithographic merit function (e.g., comprisingEPE and PPE). An example of a wavefront target driving the lithographicmetric of the DLM to determine a lens knob sub-space is illustrated anddiscussed with respect to FIG. 19 later in the disclosure. In anembodiment, lithographic metric is a function of sensitivities of theresidual aberration wavefront and measured wavefront associated with agiven lens actuator setting, the sensitivities being determined withrespect to the merit function of the patterning process.

In an embodiment, the determining of the lens knob setting 1803 is aniterative process. An iteration involves executing the lens model usinga sub-set of lens knob space to determine the aberration wavefrontassociated with an optical system of the patterning apparatus;determining, using the determined aberration wavefront, the lithographicmetric and the lens merit function; determining a gradient of the lensmerit function and/or the lithographic metric with respect to the lensknob space; and selecting, based on the gradient of the lens meritfunction and/or the lithographic metric, another subset of the lens knobspace that causes the difference to be reduced in a subsequentiteration. The iterations may continue till the lens merit functionand/or the lithographic metric is minimized or convergence (e.g., nofurther improvement in merit function) is achieved.

In an embodiment, the lithographic metric is a sum of a product of asensitivity of a lens knob setting and a given wavefront associated withthe patterning apparatus. In an embodiment, the aberration wavefront isrepresented by a Zernike polynomial. In an embodiment, the lithographicmetric is a function of a plurality of Zernike polynomials, the functionmimicking effects of changes to the lens knob setting 1803 of thepatterning apparatus. In an embodiment, the Zernike polynomials areweighted according to a correction potential of the patterningapparatus.

In an embodiment, the goal of the simulation (e.g., involving executingDLM) is to minimize the following expression (Eq. 2), where ZPC_(i)represents a reference wavefront and (Z_(i)−ZPC_(i)) represents theZernike process offset applied in the Wavefront offset solution toobtain an optimized wavefront; and where index i is a Zernike indexnumber. According to the present disclosure, the image tuning furtherincludes lithographic metric and the wavefront target 1802 that drivesthe DLM in selecting of knob sub-space in a lens knob space.

$\begin{matrix}{{{minimize}\left( \text{⁠}{{\sum\limits_{i}\left( {Z_{i} - {ZPC}_{i}} \right)^{2}} + \left( {{{lithographic}{metric}} - {{wavefront}{target}}} \right)^{2}} \right){where}{lithographic}{metric}} = {\sum\limits_{i}{s_{i} \cdot Z_{i}}}} & \left( {{Eq}.2} \right)\end{matrix}$

In an embodiment, based on an imaging and/or overlay performance (e.g.,EPE and/or PPE), some directions in lens knob space may be moreproblematic than others. In this case, a lithographic metric LiMe guidesthe DLM (via DLM's merit function) regarding what the problematicdirections. In an embodiment, one lithometric LiMe defines a hyperplanein lens knob space. If N=number of lens knobs, then N LiMe's define apoint in lens knob space with a hyerspherical merit function around it,and N weighted LiMe's define a hyperellipsoid as a merit function tobenefit some directions compared to other directions. An M (M=N−P)dimensional hyperellipsoid has P dimensions that are infinite,indicating these P dimensions of the lens knob space can be consideredirrelevant to imaging/overlay performance.

In an embodiment, the hyperellipsoid (e.g. a cigar shape in 3dimensional space) is defined by fitting a hyperellipsoid function tothe imaging or overlay merit function around a desired working point(e.g., a global minima of the lithographic merit function). In anembodiment, the fitting process employs PCA analysis to identifycombinations of fitting variables (e.g., lens knob adjustmentparameters) that explain prevalent contributors of the merit functionaround the desired working point. In an embodiment, for robustness, onlyfew PCA components may be selected. In an embodiment, a PCA componentbecomes a lithographic metric. For example, first 10 PCA components(e.g., P1-P10 out of 16 components in FIG. 17 ) may be considered as 10different lithographic metric.

In an embodiment, the fitted function cannot represent a random shapee.g. a banana shape, because the DLM may not be configured to deal withnon-linear behavior. In an embodiment, such restriction may be applieddue to timing constraint for the DLM solution associated with a scannerthroughput and a net lot overhead.

In an embodiment, the LiMe (e.g., the cigar shaped hyperellipsoid)fitting may be limited to practical aberration magnitudes. For example,apart from limiting the fitting along a lens knob axis, a weight oflarger aberration contents may be reduced, e.g. radially in lens knobspace. Further, some azimuthal angles in lens knob space may be moreimportant than others, because actual scanner aberrations (LFP, MH, andpotentially others) occur more in certain parts of the lens knobsub-space than in others. There may even be an offset of average actuallens aberration state with respect to a zeroth origin (e.g. systematiclens fingerprint, offset in slit only).

In FIG. 19 , a plot 1900 illustrates an example of determining lens knobsetting (e.g., lens knob K1 and lens knob K2) based on lithographicmetrics L1 and L2 and a wavefront target Tx. In an embodiment, thelithographic metric L1 correspond to a first wavefront (e.g., a firstPCA component) and the metric L2 correspond to a second wavefront (e.g.,PCA component). Then, based on a sensitivity of the lens knob settingsof knobs K1 and K2, a sub-space 1910 of the lens knob space K1 and K2may be identified. For example, the lithographic metric L1 is reduced(in an embodiment, minimized) when the lens knob sub-space is along orclose to line of the lithographic metric L1, while reducing (in anembodiment, minimizing) a distance from the wavefront target. Similarly,the lithographic metric L2 in combination with wavefront target Txguides the selection of appropriate sub-space from the lens knob spaceof K1 and K2.

The sub-space 1910 is an acceptable set of values of the knob setting ofK1 and K2. The sub-space 1910 is considered within an acceptable rangeof the wavefront target Tx. In an embodiment, the acceptable rangearound the wavefront target may be defined as a function of a distanceof any point in the sub-space from the wavefront target. Closer thesub-space to the wavefront target, better will be the imaging and/oroverlay performance. For example, the values of sub-space defined byregion between 1901 and 1902 are farthest away from the wavefront targetand not acceptable.

In an embodiment, the knobs K1 and K2 are lens adjustment parameter suchas a tilt (curvature, rotation, or other lens related parameter) of afirst lens and the second lens, respectively.

In an embodiment, the lithographic metric represents a physical quantityassociated with a pattern imaged, via the patterning apparatus, on asubstrate. In an embodiment, the lithographic metric represents at leastone of the following physical quantity: a pattern shift associated witha printed pattern with respect to a desired position of a desiredpattern, a focus shift of the patterning apparatus with respect to thesubstrate, the focus shift containing astigmatism offset associated withthe patterning apparatus, an asymmetry in critical dimension at a topand a bottom of the printed pattern, and/or an edge placement errorassociated with the printed pattern.

In an embodiment, the procedure P1303 of determining the lens knobsetting 1803 involves simulating the lens model such that a differencebetween the lithographic metric and the wavefront target 1802 isreduced.

In an embodiment, the procedure P1803 of the determining the lens knobsetting 1803 involves computing the sensitivities of the residualaberration wavefront and/or the measured wavefront associated with thelens actuator space; and determining the lens knob setting as a sub-setof lens knob space based on the sensitivities such that the sub-set oflens actuator space minimizes the lithographic metric, for example usingequation Eq. 2 herein.

In an embodiment, the procedure P1803 the determining of the lens knobsetting 1803 involves reducing weight of one or more Zernike polynomialsassociated with relatively higher aberration content.

In an embodiment, the determining the lens knob setting 1803 involvesdetermining a sub-set of the lens knob space to balance scanneraberrations due to lens fingerprint, and/or mirror heating, where thebalancing is based on adjusting weights of the Zernike polynomials.

Upon optimization based on lithographic metric discussed above, the DLMoutputs the lens knob setting 1803 includes values associated with anoffset, a tilt, a curvature, and/or up to and including 3^(rd) orderparameters associated with Zernike polynomials. In an embodiment,parameters higher than 3^(rd) oder may also be considered during theoptimization process. In an embodiment, procedure P1805 involvesadjusting the optical system based on the lens knob setting 1803. As aresult, the patterning apparatus using the optical system improves theyield of the patterning process.

In an embodiment, the optimization of a patterning process may beperformed in following manner: (i) a pupil optimization (e.g., usingFlexPupil) can be performed to tune overlay performance, without losingtoo much contrast of a substrate or imaging performance of thepatterning apparatus. For example, the pupil shape and intensity may beadjusted so that the contrast loss or EPE is minimized. Then, (ii) thelithographic metric based merit function (e.g., used in lens model 1301)may be used for tuning one or more critical layer of a substrate, ratherthan using the default lens merit function. For example, thelithographic metric can be used for a field size scaling in an imagetuner sub-recipe for non-full fields, thus optimizing only those slitpoints that do matter.

FIG. 20 is a block diagram that illustrates a computer system 100 whichcan assist in implementing the methods, flows or the apparatus disclosedherein. Computer system 100 includes a bus 102 or other communicationmechanism for communicating information, and a processor 104 (ormultiple processors 104 and 105) coupled with bus 102 for processinginformation. Computer system 100 also includes a main memory 106, suchas a random access memory (RAM) or other dynamic storage device, coupledto bus 102 for storing information and instructions to be executed byprocessor 104. Main memory 106 also may be used for storing temporaryvariables or other intermediate information during execution ofinstructions to be executed by processor 104. Computer system 100further includes a read only memory (ROM) 108 or other static storagedevice coupled to bus 102 for storing static information andinstructions for processor 104. A storage device 110, such as a magneticdisk or optical disk, is provided and coupled to bus 102 for storinginformation and instructions.

Computer system 100 may be coupled via bus 102 to a display 112, such asa cathode ray tube (CRT) or flat panel or touch panel display fordisplaying information to a computer user. An input device 114,including alphanumeric and other keys, is coupled to bus 102 forcommunicating information and command selections to processor 104.Another type of user input device is cursor control 116, such as amouse, a trackball, or cursor direction keys for communicating directioninformation and command selections to processor 104 and for controllingcursor movement on display 112. This input device typically has twodegrees of freedom in two axes, a first axis (e.g., x) and a second axis(e.g., y), that allows the device to specify positions in a plane. Atouch panel (screen) display may also be used as an input device.

According to one embodiment, portions of one or more methods describedherein may be performed by computer system 100 in response to processor104 executing one or more sequences of one or more instructionscontained in main memory 106. Such instructions may be read into mainmemory 106 from another computer-readable medium, such as storage device110. Execution of the sequences of instructions contained in main memory106 causes processor 104 to perform the process steps described herein.One or more processors in a multi-processing arrangement may also beemployed to execute the sequences of instructions contained in mainmemory 106. In an alternative embodiment, hard-wired circuitry may beused in place of or in combination with software instructions. Thus, thedescription herein is not limited to any specific combination ofhardware circuitry and software.

The term “computer-readable medium” as used herein refers to any mediumthat participates in providing instructions to processor 104 forexecution. Such a medium may take many forms, including but not limitedto, non-volatile media, volatile media, and transmission media.Non-volatile media include, for example, optical or magnetic disks, suchas storage device 110. Volatile media include dynamic memory, such asmain memory 106. Transmission media include coaxial cables, copper wireand fiber optics, including the wires that comprise bus 102.Transmission media can also take the form of acoustic or light waves,such as those generated during radio frequency (RF) and infrared (IR)data communications. Common forms of computer-readable media include,for example, a floppy disk, a flexible disk, hard disk, magnetic tape,any other magnetic medium, a CD-ROM, DVD, any other optical medium,punch cards, paper tape, any other physical medium with patterns ofholes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip orcartridge, a carrier wave as described hereinafter, or any other mediumfrom which a computer can read.

Various forms of computer readable media may be involved in carrying oneor more sequences of one or more instructions to processor 104 forexecution. For example, the instructions may initially be borne on amagnetic disk of a remote computer. The remote computer can load theinstructions into its dynamic memory and send the instructions over atelephone line using a modem. A modem local to computer system 100 canreceive the data on the telephone line and use an infrared transmitterto convert the data to an infrared signal. An infrared detector coupledto bus 102 can receive the data carried in the infrared signal and placethe data on bus 102. Bus 102 carries the data to main memory 106, fromwhich processor 104 retrieves and executes the instructions. Theinstructions received by main memory 106 may optionally be stored onstorage device 110 either before or after execution by processor 104.

Computer system 100 may also include a communication interface 118coupled to bus 102. Communication interface 118 provides a two-way datacommunication coupling to a network link 120 that is connected to alocal network 122. For example, communication interface 118 may be anintegrated services digital network (ISDN) card or a modem to provide adata communication connection to a corresponding type of telephone line.As another example, communication interface 118 may be a local areanetwork (LAN) card to provide a data communication connection to acompatible LAN. Wireless links may also be implemented. In any suchimplementation, communication interface 118 sends and receiveselectrical, electromagnetic or optical signals that carry digital datastreams representing various types of information.

Network link 120 typically provides data communication through one ormore networks to other data devices. For example, network link 120 mayprovide a connection through local network 122 to a host computer 124 orto data equipment operated by an Internet Service Provider (ISP) 126.ISP 126 in turn provides data communication services through theworldwide packet data communication network, now commonly referred to asthe “Internet” 128. Local network 122 and Internet 128 both useelectrical, electromagnetic or optical signals that carry digital datastreams. The signals through the various networks and the signals onnetwork link 120 and through communication interface 118, which carrythe digital data to and from computer system 100, are exemplary forms ofcarrier waves transporting the information.

Computer system 100 can send messages and receive data (from database152), including program code, through the network(s), network link 120,and communication interface 118. In the Internet example, a server 130might transmit a requested code for an application program throughInternet 128, ISP 126, local network 122 and communication interface118. One such downloaded application may provide all or part of a methoddescribed herein, for example. The received code may be executed byprocessor 104 as it is received, and/or stored in storage device 110, orother non-volatile storage for later execution. In this manner, computersystem 100 may obtain application code in the form of a carrier wave.

Referring to FIG. 21 , the illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods toproduce EUV radiation include, but are not necessarily limited to,converting a material into a plasma state that has at least one element,e.g., xenon, lithium or tin, with one or more emission lines in the EUVrange. In one such method, often termed laser produced plasma (“LPP”)the plasma can be produced by irradiating a fuel, such as a droplet,stream or cluster of material having the line-emitting element, with alaser beam. The source collector module SO may be part of an EUVradiation system including a laser, not shown in FIG. 21 , for providingthe laser beam exciting the fuel. The resulting plasma emits outputradiation, e.g., EUV radiation, which is collected using a radiationcollector, disposed in the source collector module. The laser and thesource collector module may be separate entities, for example when a CO2laser is used to provide the laser beam for fuel excitation.

In such cases, the laser is not considered to form part of thelithographic apparatus and the radiation beam is passed from the laserto the source collector module with the aid of a beam delivery systemcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thesource collector module, for example when the source is a dischargeproduced plasma EUV generator, often termed as a DPP source.

The illuminator IL may comprise an adjuster for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL maycomprise various other components, such as facetted field and pupilmirror devices. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross section.

The radiation beam B is incident on the patterning device (e.g., mask)MA, which is held on the support structure (e.g., patterning devicetable) MT, and is patterned by the patterning device. After beingreflected from the patterning device (e.g. mask) MA, the radiation beamB passes through the projection system PS, which focuses the beam onto atarget portion C of the substrate W. With the aid of the secondpositioner PW and position sensor PS2 (e.g. an interferometric device,linear encoder or capacitive sensor), the substrate table WT can bemoved accurately, e.g. so as to position different target portions C inthe path of the radiation beam B. Similarly, the first positioner PM andanother position sensor PS1 can be used to accurately position thepatterning device (e.g. mask) MA with respect to the path of theradiation beam B. Patterning device (e.g. mask) MA and substrate W maybe aligned using patterning device alignment marks M1, M2 and substratealignment marks P1, P2.

The depicted apparatus 1000 could be used in at least one of thefollowing modes:

1. In step mode, the support structure (e.g. patterning device table) MTand the substrate table WT are kept essentially stationary, while anentire pattern imparted to the radiation beam is projected onto a targetportion C at one time (i.e. a single static exposure). The substratetable WT is then shifted in the X and/or Y direction so that a differenttarget portion C can be exposed.

2. In scan mode, the support structure (e.g. patterning device table) MTand the substrate table WT are scanned synchronously while a patternimparted to the radiation beam is projected onto a target portion C(i.e. a single dynamic exposure). The velocity and direction of thesubstrate table WT relative to the support structure (e.g. patterningdevice table) MT may be determined by the (de-)magnification and imagereversal characteristics of the projection system PS.

3. In another mode, the support structure (e.g. patterning device table)MT is kept essentially stationary holding a programmable patterningdevice, and the substrate table WT is moved or scanned while a patternimparted to the radiation beam is projected onto a target portion C. Inthis mode, generally a pulsed radiation source is employed and theprogrammable patterning device is updated as required after eachmovement of the substrate table WT or in between successive radiationpulses during a scan. This mode of operation can be readily applied tomaskless lithography that utilizes programmable patterning device, suchas a programmable mirror array of a type as referred to above.

FIG. 22 shows the apparatus 1000 in more detail, including the sourcecollector module SO, the illumination system IL, and the projectionsystem PS. The source collector module SO is constructed and arrangedsuch that a vacuum environment can be maintained in an enclosingstructure 220 of the source collector module SO. An EUV radiationemitting plasma 210 may be formed by a discharge produced plasma source.EUV radiation may be produced by a gas or vapor, for example Xe gas, Livapor or Sn vapor in which the very hot plasma 210 is created to emitradiation in the EUV range of the electromagnetic spectrum. The very hotplasma 210 is created by, for example, an electrical discharge causingat least partially ionized plasma. Partial pressures of, for example, 10Pa of Xe, Li, Sn vapor or any other suitable gas or vapor may berequired for efficient generation of the radiation. In an embodiment, aplasma of excited tin (Sn) is provided to produce EUV radiation.

The radiation emitted by the hot plasma 210 is passed from a sourcechamber 211 into a collector chamber 212 via an optional gas barrier orcontaminant trap 230 (in some cases also referred to as contaminantbarrier or foil trap) which is positioned in or behind an opening insource chamber 211. The contaminant trap 230 may include a channelstructure. Contamination trap 230 may also include a gas barrier or acombination of a gas barrier and a channel structure. The contaminanttrap or contaminant barrier 230 further indicated herein at leastincludes a channel structure, as known in the art.

The collector chamber 211 may include a radiation collector CO which maybe a so-called grazing incidence collector. Radiation collector CO hasan upstream radiation collector side 251 and a downstream radiationcollector side 252. Radiation that traverses collector CO can bereflected off a grating spectral filter 240 to be focused in a virtualsource point IF along the optical axis indicated by the dot-dashed line‘0’. The virtual source point IF is commonly referred to as theintermediate focus, and the source collector module is arranged suchthat the intermediate focus IF is located at or near an opening 221 inthe enclosing structure 220. The virtual source point IF is an image ofthe radiation emitting plasma 210.

Subsequently the radiation traverses the illumination system IL, whichmay include a facetted field mirror device 22 and a facetted pupilmirror device 24 arranged to provide a desired angular distribution ofthe radiation beam 21, at the patterning device MA, as well as a desireduniformity of radiation intensity at the patterning device MA. Uponreflection of the beam of radiation 21 at the patterning device MA, heldby the support structure MT, a patterned beam 26 is formed and thepatterned beam 26 is imaged by the projection system PS via reflectiveelements 28, 30 onto a substrate W held by the substrate table WT.

More elements than shown may generally be present in illumination opticsunit IL and projection system PS. The grating spectral filter 240 mayoptionally be present, depending upon the type of lithographicapparatus. Further, there may be more mirrors present than those shownin the figures, for example there may be 1-6 additional reflectiveelements present in the projection system PS than shown in FIG. 22 .

Collector optic CO, as illustrated in FIG. 22 , is depicted as a nestedcollector with grazing incidence reflectors 253, 254 and 255, just as anexample of a collector (or collector mirror). The grazing incidencereflectors 253, 254 and 255 are disposed axially symmetric around theoptical axis O and a collector optic CO of this type may be used incombination with a discharge produced plasma source, often called a DPPsource.

Alternatively, the source collector module SO may be part of an LPPradiation system as shown in FIG. 23 . A laser LA is arranged to depositlaser energy into a fuel, such as xenon (Xe), tin (Sn) or lithium (Li),creating the highly ionized plasma 210 with electron temperatures ofseveral 10's of eV. The energetic radiation generated duringde-excitation and recombination of these ions is emitted from theplasma, collected by a near normal incidence collector optic CO andfocused onto the opening 221 in the enclosing structure 220.

The embodiments may further be described using the following clauses:

-   1. A method for determining a wavefront of a patterning apparatus of    a patterning process, the method comprising:

obtaining (i) a reference performance of a reference apparatus, (ii) alens model of a patterning apparatus configured to convert a wavefrontparameter of a wavefront to actuator movements, and (iii) a lensfingerprint of a tuning scanner; and

determining, via a processor, the wavefront parameter based on the lensfingerprint of the tuning scanner, the lens model, and a cost function,wherein the cost function is a difference between the referenceperformance and a tuning scanner performance.

-   2. The method of clause 1, wherein the determining of the wavefront    parameter is an iterative process, an iteration comprising:

generating, via simulation of the lens model using the lens fingerprintof the tuning scanner, an initial wavefront;

determining a substrate pattern from the initial wavefront;

determining the tuning performance from the substrate pattern;

evaluating the cost function based on the tuning performance and thereference performance; and

adjusting the wavefront parameter of the initial wavefront based on agradient of the cost function, such that the cost function is improved.

-   3. The method of any of clauses 1-2, wherein the wavefront comprises    the lens fingerprint of the tuning scanner and a performance    fingerprint of the lens model.-   4. The method of clause 3, wherein the adjusting of the wavefront    parameter is further based on the performance fingerprint of the    lens model.-   5. The method of any of clauses 2-4, wherein determining the    substrate pattern comprises simulation of a process model of the    patterning process using the initial wavefront or the adjusted    wavefront.-   6. The method of clause 5, wherein the process model comprises:    a mask model configured to predict a mask image based from a mask    pattern;    an optical model configured to predict an aerial image from the mask    pattern; and/or    a resist model configured to predict a resist image from the aerial    image.-   7. The method of any of clauses 2-4, wherein determining the    substrate pattern comprises:

receiving, via a metrology tool, substrate measurements of an exposedsubstrate, wherein the substrate is exposed using the initial wavefrontor the adjusted wavefront; and

determining the substrate pattern based on contour extraction from thesubstrate measurement.

-   8. The method of any of clauses 1-7, wherein the cost function is    minimized or maximized.-   9. The method of any of clauses 1-8, wherein the cost function is an    edge placement error, CD and/or an error within a tolerance band of    edge placement.-   10. The method of any of clauses 1-9, wherein the lens model    includes constraints related to a correction limitation of a tuning    scanner corresponding to a wavefront parameter.-   11. The method of any of clauses 1-10, wherein the wavefront    parameter comprises an offset, a tilt, a curvature, and/or up to    third order parameters associated with an optical system of the    patterning apparatus.-   12. The method of any of clauses 1-11, wherein the wavefront is a    through-slit wavefront.-   13. The method of clause 12, wherein the slit has a rectangular    shape.-   14. The method of any of clauses 1-13, wherein the wavefront is    represented by Zernike polynomial across a slit.-   15. The method of clause 14, wherein the wavefront parameter is    expressed as a vector of Zernike coefficients.-   16. The method of any of clauses 1-15, further comprising:

converting, via the lens model, the wavefront parameters to the actuatormovements; and

actuating the optical system of the tuning scanner based on the actuatormovements.

-   17. The method of any of clauses 1-16, wherein the reference    performance and the tuning scanner performance are expressed in    terms of a contour of a pattern and/or a critical dimension.-   18. A method for determining a wavefront of a tuning scanner with    respect to a reference apparatus, the method comprising:

obtaining (i) a reference performance of the reference apparatuscorresponding to a reference lens fingerprint, and (ii) a lensfingerprint of a tuning scanner;

determining, via a processor, a wavefront parameter of the tuningscanner based on the lens fingerprint and a cost function, wherein thecost function computes a difference between the reference performanceand a tuning scanner performance.

-   19. The method of clause 18, wherein obtaining the reference    performance comprises:

measuring the reference lens fingerprint of the reference apparatus;

generating, via simulation of a process model, a reference pattern basedon the measured lens fingerprint of the reference apparatus and apatterning device pattern corresponding to a design layout; and

determining the reference performance based on a contour of thereference pattern.

-   20. The method of any of clauses 18-19, wherein the determining of    the wavefront parameter is an iterative process, an iteration    comprising:

determining via simulation of the process model, a substrate patternusing a patterning device pattern and a lens fingerprint of the tuningscanner;

determining the tuning scanner performance based on the substratepattern;

evaluating the cost function based on the tuning scanner performance andthe reference performance; and

adjusting the wavefront parameter based on a gradient of the costfunction with respect to the wavefront parameter, such that the costfunction is improved.

-   21. The method of clause 20, wherein the patterning device pattern    is generated via simulation of a mask optimization or source mask    optimization process, wherein a lens aberration model is included in    the process model.-   22. The method of any of clauses 19-21, wherein the reference    performance and tuning scanner performance is expressed in terms of    a contour of a pattern, and/or a critical dimension.-   23. The method of any of clauses 19-22, wherein the reference    apparatus comprises:

a scanner of a wafer fabrication facility;

an ideal scanner having no aberrations; and/or

an aberration compensated scanner that is compensated for averageaberration of a plurality of scanners within the wafer fabricationfacility.

-   24. The method of any of clauses 18-23, wherein the cost function is    an edge placement error, CD and/or an error within a tolerance band    of edge placement.-   25. The method of any of clauses 18-24, wherein the wavefront    parameter comprises an offset, a tilt, a curvature, and/or up to and    including third order parameters associated with an optical system    of the patterning apparatus.-   26. A method of wavefront matching of a tuning scanner for a    patterning process, the method comprising:

obtaining (i) a plurality of hot spot patterns corresponding to a layerof a substrate, (ii) a plurality of wavefronts corresponding to theplurality of hot spot patterns, and (iii) a lens fingerprint of a tuningscanner;

determining, via simulation of a patterning process using the lensfingerprint, a tuning scanner performance; and

selecting a wavefront parameter for the tuning scanner from theplurality of wavefronts based on comparison between the tuning scannerperformance and a reference performance.

-   27. The method of clause 26, wherein one or more of the plurality of    wavefronts include optimized wavefront parameters.-   28. The method of any of clauses 26-27, wherein the one or more of    the plurality of wavefronts is associated with a particular    reference performance.-   29. A method of determining a lens adjustment parameter value for a    patterning apparatus used in a patterning process, the method    comprising:

obtaining (i) a pupil weight map associated with an exposure wavefront,wherein weights of the pupil weight map are associated with aperformance metric of the patterning apparatus, and (ii) a lens model ofa patterning apparatus, the lens model configured to convert anaberration wavefront parameter associated with the exposure wavefront toa lens adjustment parameter;

determining, via executing the lens model using the pupil weight map andthe exposure wavefront, a lens adjustment parameter value such that alens model merit function associated with the lens model is improved,wherein the lens model merit function is a function of the pupil weightmap; and

adjusting, via simulating a patterning process using the aberrationwavefront associated with the lens adjustment parameter value, theweights of the pupil weight map such that the performance metric of thepatterning process is improved, the performance metric being a functionof an edge placement error and a pattern placement error associated witha pattern to be printed on a substrate.

-   30. The method of clause 29, wherein the pupil weight map is a    pixelated image, wherein a given pixel of the pixelated image is    assigned a weight based on an impact of change in the given pixel    value on the performance metric.-   31. The method of any of clauses 29-30, wherein the weights of the    pupil weight map are based on diffraction information associated    with an illumination pupil, wherein the diffraction information    comprises diffraction orders and/or diffraction intensity pattern.-   32. The method of clause 30, wherein a portion of the pupil weight    map associated with a diffraction order is assigned a weight 1 and    another portion not associated with the diffraction order is    assigned a weight 0.-   33. The method of clause 30, wherein the diffraction intensity    pattern is a linear combination of Zernike polynomials describing    the weight.-   34. The method of any of clauses 29-34, wherein the weights of the    pupil weight map are based on Zernike sensitivities, a given Zernike    sensitivity being a partial derivative of the performance metric    with respect to a given Zernike polynomial.-   35. The method of any of clauses 29-34, wherein the weights of the    pupil weight map are based on principal component analysis (PCA) of    a set of wavefronts, the set of wavefronts obtained from one or more    scanners used in the patterning process.-   36. The method of clause 35, wherein the weights of the pupil weight    map are based on a sensitivity of a principal component of the set    of wavefronts, the sensitivity being determined with respect to the    performance metric.-   37. The method of clause 36, wherein the weights of the pupil weight    map are based on a mini-batch algorithm.-   38. The method of any of clauses 29-37, wherein the determining of    the lens adjustment parameter is an iterative process, an iteration    comprising:

executing the lens model using the pupil weight map and the givenexposure wavefront to generate the aberration wavefront;

determining, based on the aberration wavefront, the edge placement errorand the pattern placement error associated with one or more portions ofthe aberration wavefront;

evaluating the performance metric using the edge placement error and thepattern placement error; and

adjusting, via lens actuator adjustment, the aberration wavefrontparameter based on a gradient of the performance metric such that theperformance metric is improved.

-   39. The method of any of clauses 29-32, further comprising:

deweighting or upweighting a region of the illumination pupil via thepupil weight map;

executing the lens model using the deweighted pupil weight map or theupweighted pupil weight map; and

determining another lens adjustment parameter values associated with theaberration wavefront using the deweighted pupil map or the upweightedpupil map, and the exposure wavefront associated therewith so that theperformance metric is minimized.

-   40. The method of any of clauses 29-33, wherein the deweighted    region is associated with the aberration wavefront that is    correctable via a wavefront manipulator of the patterning apparatus    during the patterning process.-   41. The method of any of clauses 29-34, wherein the lens model merit    function is minimized.-   42. The method of any of clauses 29-35, wherein the lens model    includes constraints related to correction limitations of the    patterning apparatus corresponding to the aberration wavefront.-   43. The method of any of clauses 29-37, wherein the exposure    wavefront is a through-slit wavefront.-   44. The method of clause 38, wherein the slit has a rectangular    shape.-   45. The method of clause 38, wherein the slit has a curved shape.-   46. The method of any of clauses 29-36, wherein the aberration    wavefront parameter are associated with an offset, a tilt, a    curvature, and/or up to and including 3^(rd) order parameters or    higher than 3^(rd) order associated with Zernike polynomials.-   47. The method of any of clauses 29-42, further comprising:

converting, via the lens model, the aberration wavefront parameter tothe lens adjustment parameter; and

actuating the optical system of a patterning apparatus based on the lensadjustment parameter.

-   48. A method of determining lens actuator setting for a patterning    apparatus, the method comprising:

obtaining a lens merit function and a reference value assigned to aresidual aberration wavefront associated with the patterning apparatus;and

determining, via a lens model of the patterning apparatus using the lensmerit function and the reference value, the lens actuator setting fromthe lens actuator space of the patterning apparatus based on minimizingthe lens merit function, the lens merit function comprising alithographic metric associated with the residual aberration wavefront.

-   49. The method of clause 48, wherein the lens merit function is    determined based on a lithographic merit function, the lithographic    merit function comprising:

an edge placement error associated with a pattern to be imaged on asubstrate; and

a pattern placement error, the pattern placement error being a mutualshift of features in a layer, the mutual shift being relative to areference position on the substrate.

-   50. The method of any of clauses 48-49, wherein the lithographic    metric is a function of at least 2^(nd) order of the edge placement    error (EPE) and/or at least 2^(nd) order of the pattern placement    error (PPE), wherein the EPE and/or the PPE are caused due to    changes in the lens actuator setting.-   51. The method of any of clauses 48-50, wherein the reference value    is associated with one or more points at or around the global minima    of the lithographic merit function.-   52. The method of any of clauses 48-51, wherein the lithographic    metric defines a hyperplane in the lens actuator space, the    hyperplane providing a relationship between the lithographic metric    and at least two actuator settings of the lens actuator space.-   53. The method of any of clauses 48-52, wherein the determining of    the lens actuator setting is an iterative process, an iteration    comprises:

executing the lens model using a sub-set of lens actuator space todetermine the aberration wavefront;

determining, using the determined aberration wavefront, the lithographicmetric and the lens merit function;

determining a gradient of the lens merit function and/or thelithographic metric with respect to the lens actuator space; and

selecting, based on the gradient of the lens merit function and/or thelithographic metric, another subset of the lens actuator space thatcauses the lens merit function and/or the lithographic metric to bereduced in a subsequent iteration.

-   54. The method of any of clauses 46-53, wherein the lithographic    metric is a function of sensitivities of the residual aberration    wavefront and/or a measured wavefront associated with a given lens    actuator setting, the sensitivities being determined with respect to    a merit function of the patterning process.-   55. The method of clause 54, wherein the determining the lens    actuator setting comprises:

computing in the sensitivities of the aberration wavefront and/or themeasured wavefront associated with the lens actuator space; and

determining the lens actuator setting as a sub-set of lens actuatorspace based on the sensitivities such that the sub-set of lens actuatorspace minimizes the lithographic metric.

-   56. The method of any of clauses 55, wherein the aberration    wavefront is represented by Zernike polynomials.-   57. The method of clause 56, wherein the Zernike polynomials are    weighted according to a correction potential of the patterning    apparatus.-   58. The method of any of clauses 56-57, wherein the determining of    the lens actuator setting comprises:

reducing weight of one or more Zernike polynomials associated withrelatively higher aberration content.

-   59. The method of any of clauses 56-58, wherein the determining the    lens actuator setting comprises:

determining a sub-set of the lens actuator space to balance scanneraberrations due to lens fingerprint, and/or mirror heating, wherein thebalancing is based on adjusting weights of the Zernike polynomials.

-   60. The method of any of clauses 48-59, wherein the lithographic    metric represents a physical quantity associated with a pattern    imaged, via the patterning apparatus, on a substrate.-   61. The method of clause 60, wherein the lithographic metric    represents at least one of the following physical quantity:

a pattern shift associated with a printed pattern with respect to adesired position of a desired pattern,

a focus shift of the patterning apparatus with respect to the substrate,

the focus shift containing astigmatism offset associated with thepatterning apparatus,

an asymmetry in critical dimension at a top and a bottom of the printedpattern, or

an edge placement error associated with the printed pattern.

-   62. The method of any of clauses 48-61, wherein the lens actuator    setting comprises values associated with an offset, a tilt, a    curvature, and/or up to and including 3^(rd) order parameters or    higher than 3^(rd) order associated with Zernike polynomials.

The concepts disclosed herein may simulate or mathematically model anygeneric imaging system for imaging sub wavelength features, and may beespecially useful with emerging imaging technologies capable ofproducing increasingly shorter wavelengths. Emerging technologiesalready in use include EUV (extreme ultra violet), DUV lithography thatis capable of producing a 193 nm wavelength with the use of an ArFlaser, and even a 157 nm wavelength with the use of a Fluorine laser.Moreover, EUV lithography is capable of producing wavelengths within arange of 20-5 nm by using a synchrotron or by hitting a material (eithersolid or a plasma) with high energy electrons in order to producephotons within this range.

While the concepts disclosed herein may be used for imaging on asubstrate such as a silicon wafer, it shall be understood that thedisclosed concepts may be used with any type of lithographic imagingsystems, e.g., those used for imaging on substrates other than siliconwafers.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made as described without departing from the scope of the claimsset out below.

What is claimed is:
 1. A computer readable non-transitory storage mediumcomprising instructions, the instructions, when executed by a computersystem, configured to cause the computer system to at least: obtain (i)a reference performance of a reference apparatus, (ii) a lens model fora patterning apparatus configured to convert a wavefront parameter of awavefront to actuator movement, and (iii) a lens fingerprint of a tuningapparatus; and determine the wavefront parameter based on the lensfingerprint, the lens model, and a cost function, wherein the costfunction comprises a difference between the reference performance and atuning apparatus performance.
 2. The medium of claim 1, wherein theinstructions configured to cause the computer system to determine thewavefront parameter are configured to do so in an iterative process, aniteration comprising: generation, via simulation with the lens modelusing the lens fingerprint of the tuning apparatus, of an initialwavefront; determination of a substrate pattern from the initialwavefront; determination of the tuning apparatus performance from thesubstrate pattern; evaluation of the cost function based on the tuningapparatus performance and the reference performance; and adjustment ofthe wavefront parameter of the initial wavefront based on a gradient ofthe cost function, such that the cost function is improved.
 3. Themedium of claim 2, wherein the adjustment of the wavefront parameter isfurther based on a performance fingerprint of the lens model.
 4. Themedium of claim 2, wherein the determination of the substrate patterncomprises simulation with a process model of the patterning processusing the initial wavefront or the adjusted wavefront parameter-.
 5. Themedium of claim 2, wherein the determination of the substrate patterncomprises: receipt, via a metrology tool, of substrate measurements ofan exposed substrate, wherein the substrate is exposed using the initialwavefront or the adjusted wavefront parameter; and determination of thesubstrate pattern based on contour extraction from the substratemeasurement.
 6. The medium of claim 1, wherein the wavefront parametercomprises the lens fingerprint of the tuning apparatus and a performancefingerprint of the lens model.
 7. The medium of claim 1, wherein thecost function is minimized or maximized.
 8. The medium of claim 1,wherein the cost function represents an edge placement error, CD and/oran error within a tolerance band of edge placement.
 9. The medium ofclaim 1, wherein the lens model includes constraints related to acorrection limitation of an apparatus corresponding to the wavefrontparameter.
 10. The medium of claim 1, wherein the wavefront parametercomprises an offset, a tilt, a curvature, and/or up to third orderparameter associated with an optical system of the patterning apparatus.11. The medium of claim 1, wherein the wavefront is a through-slitwavefront.
 12. The medium of claim 11, wherein the slit has arectangular shape.
 13. The medium of claim 1, wherein the wavefront isrepresented by a Zernike polynomial across a slit.
 14. The medium ofclaim 13, wherein the wavefront parameter is expressed as a vector ofZernike coefficients.
 15. The medium of claim 1, wherein theinstructions are further configured to cause the computer system to:convert, via the lens model, the wavefront parameter to the actuatormovement; and actuate the optical system of the tuning apparatus basedon the actuator movement.
 16. A computer readable non-transitory storagemedium comprising instructions, the instructions, when executed by acomputer system, configured to cause the computer system to at least:obtain (i) a reference performance of a reference apparatuscorresponding to a reference lens fingerprint, and (ii) a lensfingerprint of a tuning apparatus; and determine a wavefront parameterof the tuning apparatus based on the lens fingerprint and a costfunction, wherein the cost function computes a difference between thereference performance and a tuning apparatus performance.
 17. The mediumof claim 16, wherein the instructions configured to cause the computersystem to obtain the reference performance are further configured tocause the computer system to: obtain a measurement of the reference lensfingerprint of the reference apparatus; generate, via simulation with aprocess model, a reference pattern based on the measured reference lensfingerprint and a patterning device pattern corresponding to a designlayout; and determine the reference performance based on a contour ofthe reference pattern.
 18. The medium of claim 16, wherein theinstructions configured to cause the computer system to determine thewavefront parameter are configured to do so in an iterative process, aniteration comprising: determination via simulation with a process model,a substrate pattern using a patterning device pattern and a lensfingerprint of the tuning apparatus; determination of the tuningapparatus performance based on the substrate pattern; evaluation of thecost function based on the tuning apparatus performance and thereference performance; and adjustment of the wavefront parameter basedon a gradient of the cost function with respect to the wavefrontparameter, such that the cost function is improved.
 19. The medium ofclaim 18, wherein the patterning device pattern is generated viasimulation of a mask optimization or source mask optimization process,wherein a lens aberration model is included in the process model.
 20. Acomputer readable non-transitory storage medium comprising instructions,the instructions, when executed by a computer system, configured tocause the computer system to at least: obtain (i) a plurality of hotspot patterns corresponding to a layer of a substrate, (ii) a pluralityof wavefronts corresponding to the plurality of hot spot patterns, and(iii) a lens fingerprint of a tuning apparatus; determine, viasimulation of a patterning process using the lens fingerprint, a tuningapparatus performance; and select a wavefront parameter for the tuningapparatus from the plurality of wavefronts based on comparison betweenthe tuning apparatus performance and a reference performance.